Question

I am stuck on this oscillation problem. Sorry it asks for allot of information.
Thank You

Answer 1

Contact me when you have time and I can help you through this

Answer 2

I think the frequency f is:
\[f=\frac{ 70 }{ 131 }=0.53 Hz\]

Answer 3

yes, if the mass completes 70 oscillations in 131s, then it will complete 70/131 oscillations in one second, so that is the frequency f
the next step might be to write down an expression for the position of the mass as a function of time, since you know the frequency and amplitude - can you do this ?

Answer 4

@ProfBrainstorm In order to find the relationship between the position x(t) function of time, it is necessary to solve the subsequent ordinary differential equation:
\[mx''+kx=0\]
where m is the mass of the oscillating body, and k is the spring constant.
Now a solution of the above ODE is:
\[x(t)=A \cos(\omega t+\phi)\]
wher A is the amplitude of the oscillations and phi is an arbitrary constant, furthermore, omega is the angular frequency, namely:
\[\omega=2 \pi f=\sqrt{\frac{ k }{ m }}\]
so your frequency is:
\[f=\frac{ 1 }{ 2 \pi }\sqrt{\frac{ k }{ m }}\]
If we write the inverse formula of the last formula, in order to find k, we have:
\[k=4 \pi f ^{2}m\]
please, try to substitute your values to find the values of k.

Answer 5

Sorry, an error is occurred:
\[k=4 \pi ^{2}f ^{2}m\]

Answer 6

f and k both worked any idea about the others?

Answer 7

Managed to get the rest with the help of a friend thank you.

Answer 8

@c_c_mill thank you!