At what displacement are Kinetic energy and potential energy equal, for a body executing simple...
Question:
At what displacement are Kinetic energy and potential energy equal, for a body executing simple harmonic motion?
Energy in Simple Harmonic Motion:
The total energy of an object in simple harmonic motion is the summation of its kinetic energy and potential energy and directly proportional to the mass and square of the angular velocity of the object.
Answer and Explanation: 1
Become a Study.com member to unlock this answer! Create your account
View this answer
The Kinetic energy of the body in SHM,
{eq}\displaystyle KE = \dfrac{1}{2}m{\omega ^2}\left( {{A^2} - {x^2}} \right){/eq}
The Potential energy of...
See full answer below.
Ask a question
Our experts can answer your tough homework and study questions.
Ask a question Ask a questionSearch Answers
Learn more about this topic:

from
Chapter 11 / Lesson 2Learn what is meant by the term simple harmonic motion. Explore the characteristic of harmonic oscillations, and follow examples to calculate the amplitude and period of a harmonic oscillation.
Related to this Question
- At what displacement of a simple harmonic oscillation is the energy half kinetic and half potential?
- When the displacement in SHM is 0.4 times the amplitude A, what fraction of the total energy is kinetic energy? What fraction of the total energy is potential energy? At what displacement, in terms of
- An object spring system moving with simple harmonic motion has an amplitude A. (a) What is the total energy of the system in terms of k and A only? (b) Suppose at a certain instant the kinetic energy is twice the elastic potential energy. Write an equatio
- If the maximum kinetic energy of a simple pendulum is K, then what is its displacement (in terms of amplitude a), when its kinetic energy is K/2?
- When the displacement in SHM is equal to \frac{1}{3} of the amplitude xm, what fraction of the total energy is (a) kinetic energy and (b) potential energy? (c) At what displacement, in terms of the a
- An object executes simple harmonic motion with an amplitude A. a) At what values of its position does its speed equal half its maximum speed? b) At what values of its position does its potential energy equal half the total energy?
- When the displacement in SHM is 0.4 the amplitude A, what fraction of the total energy is kinetic energy? What fraction of the energy is potential energy? At what displacement, in terms of the amplitu
- When the displacement of a mass on a spring is one-third of A, what fraction of energy is kinetic energy and what fraction is potential energy? At what displacement, as a fraction of A, is the energy one-third kinetic and two-thirds potential?
- When the displacement in SHM is equal to \frac{1}{8} of the amplitude xm, what fraction of the total energy is (a) kinetic energy (b) potential energy? (c) At what displacement, in terms of the a
- The motion of a mass connected to a spring is described by the equation (in SI units): x = 12 sin(3.49t + 1.047). a) What is the period of oscillation? b) What is the positive displacement x when the kinetic energy equals the potential energy? c) At w
- The motion of a mass connected to a spring is described by the equation (in SI units) x = 12 sin(3.12t + 1.047). a) What is the period of oscillation? b) What is the positive displacement x when the kinetic energy equals the potential energy? c) At what
- An object of mass m attached to a spring of force constant k oscillates with simple harmonic motion. The maximum displacement from equilibrium is A and the total mechanical energy of the system is E. What is the object's velocity when its potential energy
- When the displacement in SHM is equal to 1/5 of the amplitude x_m, what fraction of the total energy is (a) kinetic energy and (b) potential energy? (c) At what displacement, in terms of the amplitude
- An object-spring system moving with simple harmonic motion has an amplitude ''A''. When the kinetic energy of the object equals twice the potential energy stored in the spring, what is the position ''
- A particle executes simple harmonic motion with an amplitude of 10 cm. Calculate at what distance from the mean position is the kinetic and potential energies equal.
- The motion of a particle connected to a spring is described by x = 10 sin(pi*t). At what time (in s) is the potential energy equal to the kinetic energy? a. 0 b. 0.25 c. 0.50 d. 0.79 e. 1.0
- a. When the displacement in SHM is one-half the amplitude x_m, what fraction of the total energy is kinetic energy? b. What fraction is potential energy? c. At what displacement, in terms of the ampl
- A 0.2 kg object is suspended from a spring with a spring constant of k = 10 n/m. The object moves with simple harmonic motion and has an amplitude of 0.08 m. What is the potential energy of the system
- Find the displacement from equilibrium for a simple harmonic oscillator if the total energy is 1 / 2 kinetic energy and 1 / 2 potential energy.
- a) When the displacement of a mass on a spring is 0.5 A, what fraction of energy is kinetic? What fraction is potential? b) At what displacement, as a fraction of the amplitude, is the energy equally
- A spring + mass oscillates with simple harmonic motion about the point y = 0. When the mass is located at y = y_{max}/3, what is the ratio of kinetic energies, k/k_{max}?
- An object-spring system moving with simple harmonic motion has an amplitude A. (a) What is the total energy of the system in terms of k and A only? E = _____ (b) Suppose at a certain instant the kinetic energy is twice the elastic potential energy. Write
- Consider a simple harmonic oscillation with m=0.5kg, k=10N/m and amplitude A= 3cm. What is the total energy of the oscillation, what is the maximum speed, what is the kinetic energy?
- When the displacement of a mass on a spring is 0.515 of the amplitude of its oscillation, what fraction of the mass s energy is kinetic energy? thanks
- A frictionless pendulum of length 3 m swings with an amplitude of 10 deg. At its maximum displacement, the potential energy of the pendulum is 10 J. What is the kinetic energy of the pendulum when its
- Calculate the ratio of the kinetic energy to the potential energy of a simple harmonic oscillator when its displacement is 1/8 of its amplitude. (The answer is an integer.) Approach: Choose a specific
- A 2 kg object undergoes simple harmonic motion with an amplitude of 0.19 m and a maximum acceleration of 4 \ m/s^2. What is its energy?
- When does kinetic energy equal potential energy in a spring?
- A particle executes simple harmonic motion with an amplitude of 10 cm. At what distance from the mean position are the kinetic and potential energies equal?
- A horizontal spring-block oscillator is in simple harmonic motion of amplitude A. What is the ratio of the kinetic energy to the elastic potential energy, KE/PE, when the displacement of the block is A/2?
- When an object moving in simple harmonic motion is at its maximum displacement from equilibrium point, which of the following is at a maximum? (a) velocity (b) acceleration (c) kinetic energy (d) total energy
- A certain pendulum has a potential energy of 20 J when it is at the top of its swing. (a) What is the kinetic energy? (b) When the pendulum reaches a certain point in its downward motion it has a
- At what displacement from the equilibrium is the total energy of a simple harmonic oscillator 1/6 KE and 5/6 PE? Answer should be in terms of the amplitude A.
- An object-spring system moving with simple harmonic motion has an amplitude A. Does the total energy change if the mass is doubled but the amplitude isn't changed? Yes or No. Are the kinetic and potential energies at a given point in its motion affected b
- When the displacement in SHM is one half the amplitude x_m: (a) What fraction of the total energy is kinetic energy? (b) What fraction is potential energy? (c) At what displacement, in terms of the amplitude, is the energy of the system half kinetic energ
- When the displacement of a mass on a spring is 12A the half of the amplitude, what fraction of the mechanical energy is kinetic energy At what displacement, as a fraction of A, is the mechanical energ
- A 2.5 kg particle is in simple harmonic motion in one dimension and moves according to the equation x = (6.4 m)cos[(π/3 rad/s)t - π/4 rad]. (a) At what value of x is the potential energy of the particle equal to half the total energy? (b) How long
- (a) When the displacement in SHM is four-fifths the amplitude x_m , what fraction of the total energy is kinetic energy? (b) What fraction is potential energy? (c) At what displacement, in terms of
- (A) When the displacement of a mass on a spring is 12 \ A the half of the amplitude, what fraction of the mechanical energy is kinetic energy? (B) At what displacement, as a fraction of A , is the me
- The simple harmonic motion of a 300 g mass on a spring is described by y = 20 cm sin(1.2566t). At t = 1/8 s what is the total energy? 1. 9000 J 2. 9.47 mJ 3. 7.5 mJ 4. 3840 J
- The motion of a particle connected to a spring is described by x= 10sin(\pi t + \pi /3). At what time (in s) is the potential energy equal to the kinetic energy?
- The displacement of a certain object of mass 9.4 kg undergoing a simple harmonic motion varies with time according to the equation x = 0.94 cos (87.5t - 2.9). Calculate its mechanical energy after 8 s
- An object has a mass of 0.5kg. It undergoes a simple harmonic motion. The amplitude of that motion is 0.07m, and the period is 0.31s. What is the total energy of the object?
- An object having mass m is attached to a spring of force constant K oscillates with simple harmonic motion. The total mechanical energy of the system is E and the maximum displacement from equilibrium is A. What is the system's potential energy when it's
- Describe the energy variation of a simple pendulum when it is performing the simple harmonic motion.
- A mass oscillates with SHM of amplitude A and period T_ y = A \cos (2\pi t/T). The kinetic energy of the mass is equal with twice the potential energy of the spring at [{Blank}].
- A 1.5 kg mass is attached to a spring with a spring constant of 110N/m. It is stretched 2.5 cm and released. What is the period of the simple harmonic motion? What is the potential energy stored in t
- A 0.20kg mass is oscillating on a spring over a horizontla frictionless surface. When it is at a displacement of 2.6cm for equilibrium it has a kinetic energy of 1.4J and a spring potential energy of
- A 0.289 kilograms mass is attached to a spring and undergoes simple harmonic motion with a period of 0.64 seconds. The total energy of the system is 4.3 Joules. What is the amplitude of the motion?
- The motion of a particle connected to a spring is described by x = 10 cos(pi t). At what time (in s) is the potential energy equal to the kinetic energy?
- The motion of a block-spring system is described by x(t)=Asin(\Omega;t). Find \Omega, if potential energy equals the kinetic energy at t =1.00 s.
- A 1.30 kg mass oscillates according to the equation x=0.650 cos(8.40t), where x is in meters and t is in seconds. A) Determine the kinetic energy when x = 0.410 m. B) Determine the potential energy
- A mass m at the end of a spring of spring constant k is undergoing simple harmonic oscillations with amplitude A. At what positive value of displacement x in terms of A is the potential energy 1/9 of the total mechanical energy?
- When the displacement in SHM is 0.3 the amplitude A: (A) What fraction of the total energy is kinetic energy? (B) What fraction of the total energy is potential energy? (C) At what displacement, in terms of amplitude, is the energy of the system half-kine
- What formula would be used to directly calculate the kinetic energy of an object with mass m bouncing up and down on a spring with spring constant k?
- A mass on a spring in simple harmonic motion has amplitude ''A'' and period ''T''. Assuming that the system has no loss of energy, at what point in the motion is the kinetic energy maximized?
- What is the period of the kinetic or the potential energy change if the period of position change of an object attached to a spring is 4.8 s ?
- An object spring system undergoes simple harmonic motion with an amplitude A. Does the total energy change if the mass is doubled but the amplitude isn't changed? Are the kinetic and potential energies at a given point in its motion affected by the change
- A object-spring system undergoes simple harmonic motion with an amplitude of A. Does the total energy change if the mass is doubled but the amplitude is not changed? Do the kinetic and potential energ
- (a) When the displacement in SHM is one-half the amplitude xm, what fraction of the total energy is kinetic energy? (b) What fraction of the total energy is kinetic energy?
- An object is oscillating with amplitude A at the end of a spring. How far (in terms of A) is this object from the equilibrium position of the spring when the elastic potential energy equals the kinetic energy?
- A particle undergoes a simple harmonic motion with an amplitude A and a total energy E. When the displacement is one-third the amplitude (x = plus-minus A/3), the ratio of the kinetic energy K to the total energy E is: (a) K/E = 1/4, (b) K/E = 15/16, (c)
- A mass-spring oscillating system undergoes SHM with amplitude A. At what location from the equilibrium point will the kinetic energy of the system equal its potential energy? (A) X = A / 2 (B) X = A / square root of 2 (C) X = A / 4 (D) X = A / 3
- The toy on a spring illustrate energy conversion among what different forms? a.Gravitational potential energy, kinetic energy, and elastic potential energy b.Gravitational potential energy, kinetic
- The kinetic energy of an object attached to a horizontal ideal spring is denoted by KE and the elastic potential energy by PE. For the simple harmonic motion of this object the maximum kinetic energy
- A 0.20-kg mass is oscillating on a spring over a horizontal frictionless surface. When it is at a displacement of 2.6 cm for equilibrium it has a kinetic energy of 2.4 J and a spring potential energy
- A body of mass 10 g oscillates with Simple Harmonic Motion of amplitude 4 cm and time period 0.50 s. Calculate: a The maximum acceleration. b The maximum kinetic energy.
- A 0.20-kg object is oscillating on a spring with a spring constant of k = 15 N/m. What is the potential energy of the system when the object displacement is 0.040 m, exactly half the maximum amplitude?
- A block-spring system undergoes simple harmonic motion with an amplitude A. Does the total energy change if the mass is doubled but the amplitude is not changed? Do the kinetic and potential energies depend on the mass?
- The figure shows the potential energy (black) and the total energy (red) of a particle oscillating on a spring. The total energy of the particle is 4 J. What is the particle's maximum kinetic energy?
- A 0.339 kg mass is attached to a spring and undergoes simple harmonic motion with a period of 0.472 seconds. The total energy of the system is 1.3 Joules. Find the amplitude of the motion. Answer in units of m.
- What is the energy of a pendulum (L = 1.70 m, m = 0.315 kg) oscillating with an amplitude of 2.0 cm?
- A mass attached to the spring oscillates with an amplitude A. A) What percentage of the energy is potential when the spring is at A/2? B) What is the position of the spring when the energy is 50% potential?
- Choose the best answer to the following: The potential energy of a compressed spring and the potential energy of a charged object both depend on (a) the work done on them. (b) motion. (c) Both of these. (d) Neither of these.
- What is simple harmonic motion, or SHM?
- What is Simple Harmonic Motion (SHM)?
- A particle of mass 0.3 kg vibrates with a period of 2 sec. if its amplitude is 0.5m what is its maximum kinetic energy?
- A mass on a spring in simple harmonic motion has amplitude ''A'' and period ''T''. Assuming that the system has no loss of energy, at what point in the motion is the potential energy maximized?
- The equation of a SHM of a 600 g object is given as x = 0.45 cos 6.4 t where the displacement x is in meters and time in seconds. What is the total energy of the system?
- An object of mass 6 kg is undergoing simple harmonic motion represented by the graph of displacement versus time shown below. If the amplitude of the motion is 9 m, what is the maximum velocity of the mass?
- Below is the position graph for a mass 5 kg mass hanging from a vertical spring undergoing simple harmonic motion similar to what we plotted in the lab. At what value(s) of the position of the mass will the kinetic and potential energies b equal? Justify
- A spring of mass m is pulled from both sides such that is gets velocity v at both ends. What will be its kinetic energy?
- (A) When the displacement of a mass on a spring is one-eighth of A, what fraction of the energy is kinetic energy and what fraction is potential energy? (B) At what displacement, as a fraction of A, i
- A 2.00kg mass is connected to a spring constant of 6.00N/m. The displacement is given by the expression x(t) = 12.0cm \sin(t). What is the maximum velocity of the simple harmonic motion?
- The motion of a 200 g particle is described by x(t) = 5.0 cm cos (50 pi t + (pi/3)) with x in cm and t in seconds. Determine the time when the potential energy is twice the kinetic energy.
- An object has a mass of 0.3\ \mathrm{kg}. It undergoes a simple harmonic motion. The amplitude of that motion is 0.09\ \mathrm{m} and the period is 0.36\ \mathrm{s}. What is the total energy of the object?
- A 0.102 kg mass is attached to a spring and executes simple harmonic motion with a period of 0.61 s. The total energy of the system is 0.6 J. Find the amplitude of the motion.
- A 357 g object attached to a horizontal spring move in simple harmonic motion with a period of 0.220 s. The total mechanical energy of the spring mass system is 5.06 J. What is the amplitude of the motion (in m)?
- A mass is oscillating with amplitude A at the end of a spring. How far (in terms of A) is this mass from the equilibrium position of the spring when the elastic potential energy equals the kinetic energy?
- A pendulum is swinging back and forth. At its lowest point it has a speed of 4\ \mathrm{m/s}. It has a mass of 1\ \mathrm{kg}. a. How much KE does it have at it's lowest point? b. At its highest point it is not moving. How much potential energy does it
- A mass m at the end of a spring of spring constant k is undergoing simple harmonic oscillations with amplitude A. a) At what positive value of displacement x in terms of A is the potential energy 1/9 of the total mechanical energy? b) What fraction of t
- A 2.9 kg object oscillates with simple harmonic motion on a spring of force constant 430.0 N/m. The maximum speed is 0.8 m/s. What is the total energy of the object and the spring?
- A mass is pushed against a spring, compressing the spring. What are the amount of potential energy acquired by the spring, and the kinetic energy and velocity of the mass after it is released?
- A mass m at the end of a spring of spring constant k is undergoing simple harmonic oscillations with amplitude A. a) At what positive value of displacement x in terms of A is the potential energy 1/9 of the total mechanical energy? b) What fraction of
- Below is the position graph for a mass 5 kg mass hanging from a vertical spring undergoing simple harmonic motion similar to what we plotted in the lab. What is the value of the position of the mass when the kinetic energy is maximum? What is the potenti
- Show that for a particle in linear SHM, the average kinetic energy over a period of oscillation equals the average potential energy over the same period.
- A force of 520 N keeps a certain spring stretched a distance of 0.200 m. (a) What is the potential energy of the spring when it is stretched 0.200 m? (b) What is the potential energy when it is compr
- The total energy of a particle, executing simple harmonic motion is
- Consider a simple harmonic oscillation with m = 0.5 kg, k = 10 N/m and amplitude A = 3 cm. What is the total energy of the oscillation?