Question

An object with mass 0.190 kg is acted on by an elastic restoring force with force constant 10.3 N/m. The object is set into oscillation with an initial potential energy of 0.150 J and an initial kinetic energy of 6.90×10⁻² J.

A) What is the amplitude of oscillation?

Express your answer with the appropriate units.

A=

B) What is the potential energy when the displacement is one-half the amplitude?

Express your answer with the appropriate units.

U=

C) At what displacement are the kinetic and potential energies equal?

Express your answer with the appropriate units.

x=

D) What is the value of the phase angle ϕ if the initial velocity is positive and the initial displacement is negative?

Express your answer in radians.

phi =

Answer 1

Hi,

Hope you are doing well.

__________________________________________________________________________

PART A:

Given that,

Initial kinetic energy,

Initial potential energy,

Therefore, Total energy,

Force constant,

From Law of conservation of energy, we have,

Therefore Amplitude is given by:

__________________________________________________________________________

PART B:

Given that, Displacement of the object,

Therefore, Potential energy is given by

__________________________________________________________________________

PART C:

Given that, Kinetic energy = potential energy.

Therefore, Potential energy= (1/2) Total energy

__________________________________________________________________________

PART D:

Initially at, t = 0 s

We have, Initial potential energy,

Therefore, Initial displacement is given by:

Given that, Initial displacement is negative,

We have, Displacement of a simple harmonic motion is given by:

If you are facing any kinds of difficulties, Please let me know. I'm here to help you! Thank you.
__________________________________________________________________________

Hope this helped for your studies. Keep learning. Have a good day.

Feel free to clear any doubts at the comment section.

Please don't forget to give a thumps up.

Thank you. :)