Hey, so I am just working on a second year Analytical Mechanics assignment, and right now dealing with oscillations. I have two questions I am stumped on and don't know if I have it right. It is probably basic, but just checking.(adsbygoogle = window.adsbygoogle || []).push({});

6. The frequency f_{d}of a damped oscillator is 100 Hz, and the ratio of

the amplitudes of two successive maxima is one half. What is the

undamped frequency f_{0}of this oscillator?

e^{-[itex]\gamma[/itex]Td}= [itex]\frac{1}{2}[/itex]

[itex]\gamma[/itex] = [itex]\frac{1}{T_{d}}[/itex]ln 2

f_{d}ln 2

[itex]\varpi[/itex]_{d}= ([itex]\varpi[/itex]_{0}^{2}- [itex]\gamma[/itex]^{2})^{[itex]\frac{1}{2}[/itex]}

[itex]\varpi[/itex]_{0}= ([itex]\varpi[/itex]_{d}^{2}+ [itex]\gamma[/itex]^{2})^{[itex]\frac{1}{2}[/itex]}

f_{o}= [f_{d}^{2}+ [itex]\frac{\gamma}{2\pi}[/itex]^{2}]^{[itex]\frac{1}{2}[/itex]}

= f_{d}[1+([itex]\frac{ln2}{2\pi}[/itex])^{2}]^{[itex]\frac{1}{2}[/itex]}

f_{o}= 100.6Hz

Is this correct?

7. An overdamped harmonic oscillator with ω_{0}= γ/2 is kicked out of equi-

librium x(t = 0) = 0 with the initial velocity v_{0}. Find the displacement

x of the oscillator at time t = (2γ)^{-1}.

As with this one, I don't know where to begin. Anyone be able to give me a hand starting it?

Cheers

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# Hey, so I am just working on a second year Analytical Mechanics

Can you offer guidance or do you also need help?

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