A mass m at the end of a spring of spring constant k is undergoing simple harmonic oscillations with amplitude A.

Question

Question

Part (a) At what positive value of displacement x in terms of A is the potential energy 1/9 of the total mechanical energy?

Part (b) What fraction of the total mechanical energy is kinetic if the displacement is 1/2 the amplitude?

Part (c) By what factor does the maximum kinetic energy change if the amplitude is increased by a factor of 3?

Answer 1

Answer #1

As total mechanical energy is constant , total mechanical energy of the system is equal to the potential energy when kinetic energy is zero.

(a)

potential energy is 1/9 of total mechanical energy implies,

(b)

Fraction of kinetic energy is given by,

(c)

Maximum kinetic energy is proportional to square of amplitude.

Therefore when amplitude is increased by a factor of 3, kinetic energy gets increased by factor of 9.

Answer 2

Similar Homework Help Questions

A mass at the end of a spring is undergoing simple harmonic oscillations with amplitude A....

A mass at the end of a spring is undergoing simple harmonic oscillations with amplitude A. a) What fraction of the total mechanical energy is kinetic if the displacement is ⅓ the amplitude? a) In terms of A, find the value of displacement x at which the potential energy equals 1 /16 of the total mechanical energy.
A mass m on a spring of stiffness k undergoes horizontal simple harmonic motion with amplitude...

A mass m on a spring of stiffness k undergoes horizontal simple harmonic motion with amplitude A, centered around x = 0. a) What is the total "mechanical" energy (kinetic plus potential) of the mass-spring system? b) What is the value of x when the mass-spring system has twice as much kinetic energy as potential energy? Your answers should be in terms of the quantities m, k, and A--or some subset thereof.
1) A 12.3 kg particle is undergoing simple harmonic motion with an amplitude of 1.86 mm....

1) A 12.3 kg particle is undergoing simple harmonic motion with an amplitude of 1.86 mm. The maximum acceleration experienced by the particle is 7.93 km/s2. (a) Find the period of the motion. (b) What is the maximum speed of the particle? (c) Calculate the total mechanical energy of this simple harmonic oscillator. 2) The orbit of the Moon around the Earth as projected along a diameter can be viewed as simple harmonic motion. Calculate the effective force constant k...

an object of mass "m" is attached to a spring with spring constant "k" and oscillated...

an object of mass "m" is attached to a spring with spring constant "k" and oscillated with simple harmonic motion motion. the maximum displacement from equillibrium is "A" and the total mechanical energy of the system is "ME." What is the system's potential energy when its kinetic energy is equal to 1/3 ME? (the answer should only have "k" and "A" as veriables, nothing else is allowed)
A spring-mass system is in simple harmonic motion. How do the period, maximum speed, frequency, and...

A spring-mass system is in simple harmonic motion. How do the period, maximum speed, frequency, and total mechanical energy of the oscillator change after each of the following alterations (up, down or no change): a) Spring constant (k) is increased? b) Amplitude id increased? c) Mass is decreased?
A mass m = 3 kg is attached to a spring with spring constant k =...

A mass m = 3 kg is attached to a spring with spring constant k = 3 N/m and oscillates with simple harmonic motion along the x-axis with an amplitude A = 0.10 m. (a) What is the angular frequency  of this oscillation? (b) What is the period T and the frequency f of the oscillation? (c) If the phase constant  = 0, write down expressions for the displacement, velocity and acceleration of the mass as a function...

For a simple harmonic oscillator of a mass attached to a spring, if its oscillation amplitude...

For a simple harmonic oscillator of a mass attached to a spring, if its oscillation amplitude is doubled, how will the following quantities change? 1) The maximum force on the mass; 2) the maximum kinetic energy of the mass; 3) the oscillation period.
Question 7 1 pts A block attached to a spring is undergoing simple harmonic motion. At...

Question 7 1 pts A block attached to a spring is undergoing simple harmonic motion. At one point in its motion, its kinetic energy is 5 J and its potential energy is 3 J. When the block reaches the point of maximum displacement from equilibrium, the kinetic and potential energies are: K-0 and U--8 Previous Submit Quiz No new data to save. Last checked at 10:39am
1. A simple harmonic motion of an object of mass m = 11 kg attached with...

1. A simple harmonic motion of an object of mass m = 11 kg attached with a spring is represented as time vs displacement graph in the following figure. Find the following parameters. ТАЛААР (a) Amplitude = (b) Time Period =( time for 1 wavelength distance) (c) Frequency = (d) Spring Constant = (e) Angular frequency = (1) Maximum Potential Energy stored in the spring (g) Maximum Kinetic Energy of the block (h) total energy of the spring -block system

1. A simple harmonic motion of an object of mass m = 11 kg attached with...

1. A simple harmonic motion of an object of mass m = 11 kg attached with a spring is represented as time vs displacement graph in the following figure. Find the following parameters. (a) Amplitude = (b) Time Period = ( time for 1 wavelength distance) (c) Frequency = (d) Spring Constant = (e) Angular frequency = (f) Maximum Potential Energy stored in the spring (g) Maximum Kinetic Energy of the block (h) total energy of the spring -block system