Solving Problems Involving Simple Harmonic Oscillators

[dalitwil]

I have two questions:

#1.) The velocity of a simple harmonic oscillator is given by
v=-7.22(26.0t) (mks units)

If the mass is 0.29kg, what is the spring's potential energy at the time t=40.33?

MY WORK:
First I found k by using ω^2=k/mass. This equaled 196.04.

I couldn't really figure out how I was supposed to derive aplitude (A) for that, So i figured since v=-Aω sin (ωt) that A =7.22/2.60.

Then i took my (probably not right) amplitude and put it into U=.5kA^2cos^2(ωt).

*This didn't work out, possibly because I can't figure out how to get the correct amplitude??

#2.) A 0.28 kg mass is attached to a vertical spring with a spring constant 9.1 N/m and let fall. What is the amplitude of the resulting motion?

MY WORK:
Since its a vertical spring, i used the equation: y0=mg/k. When I got the y0, i figured this to be twice my aplitude, so i divided it by 2.

*Wrong, again because I have issues with amplitude.

Please help me!

 

[ramollari]

I have two questions:

#1.) The velocity of a simple harmonic oscillator is given by
v=-7.22(26.0t) (mks units)

This is not the equation of velocity in SHM. It is of the form v = kt, i.e. it describes motion at constant velocity.

#2.) A 0.28 kg mass is attached to a vertical spring with a spring constant 9.1 N/m and let fall. What is the amplitude of the resulting motion?

MY WORK:
Since its a vertical spring, i used the equation: y0=mg/k. When I got the y0, i figured this to be twice my aplitude, so i divided it by 2.

*Wrong, again because I have issues with amplitude.

Please help me!

You are in the wrong track. It will be more feasible for you to use the law of conservation of Energy:

$$PE_{G1} + PE_{E1} = PE_{G2} + PE_{E2}$$

 

[dalitwil]

I am still completely clueless as to how to get the Amplitude. If I could figure that out, the problem #1 would be much easier to work out. I figure you could use the time t given to get a numerical value for velocity, but how can I relate that to A with other knowns I have?

I am not able to make sense of an equation in that form, and what exactly it means. Also, my professor isn't very willing to help with the students, so I have essentially no other resources.

Any help at all would be immensly appreciated.

 

[ramollari]

*sigh*
As I said you cannot determine the amplitude A, given only the equation of velocity which is wrong (v = kt)! Try to revisit the question, or ask your professor about the correct equation of v(t), and post it here again. Good luck!

 

[Nylex]

If you know x(t) = Acos ωt (as you used it to get PE), why isn't your velocity, v(t) = -Aωsin ωt??