Simple Harmonic Motion

Question

In a mass-spring system if m=0.25 kg, k=100 N/m, and A=0.10 m, what is the maximum speed?

Answer 1

This is the fifth question you've asked in the last twenty minutes, and you have never yet answered a single question. Why don't you try helping out with other answers?

Then why do you ask for the answer and not concept? The answer will get you nowhere.

Answer 2

Let x = A sin(wt); where x is spring displacement over time t at angular velocity w, with amplitude A.

From this we see that max displacement from neutral is A = .1 m.  At this point, the spring's potential energy max = PE = 1/2 kA^2.

Then all that PE is converted to max KE = 1/2 mV^2; where m = .25 kg and V = ? the max velocity you're looking for.

From the conservation of energy PE = 1/2 kA^2 = 1/2 mV^2 = KE; so that kA^2/m = V^2 and V = A sqrt(k/m); you can plug in the numbers.

The physics is this...the max PE = max KE from the conservation of energy law.  And A, the amplitude, is the max displacement where PE is max.