# Maximum velocity of a mass undergoing SHM

1. Apr 27, 2014

### KiNGGeexD

Question; A 1 g mass is suspended by a spring and executes simple harmonic motion when released. At time t=0 the displacement is 40 cm and acceleration is -3.6 cm/s^2. What is the spring constant k? What is the maximum velocity of this mass? At what time would the modulus of the maximum velocity first be reached?

My attempt:

I done the first part of the question and found k to be 0.025 N/m

Maximum velocity occurs when

v = ωA, and at t=0 x=A?

So hence maximum velocity would be 2 m/s

Using ω^2= k/m

Assuming the above is correct, maximum velocity would first be reached when the

sin(ωt) term is first equal to zero?

Any help would be great :) thanks

2. Apr 27, 2014

### paisiello2

You assumed that the displacement at time t=0 was the equilibrium displacement but given that there is an acceleration then this can't be the case.

Imagine the spring hanging without the mass. Then y'=0.

Next, hang the mass on the spring. Then y'= mg/k.

Lastly, pull the mass down to y'=40cm and release at t=0.

Set y = y' - mg/k and A = 40cm-mg/k.

Last edited: Apr 27, 2014
3. Apr 27, 2014

### KiNGGeexD

Ahh ok! I also realised I made an error in saying the cosine term would be equal zero, it would equal one at maximum velocity!! And thanks I will get on it right away

4. Apr 27, 2014

### KiNGGeexD

Wouldn't the amplitude be

A= y' + mg/k

5. Apr 27, 2014

### KiNGGeexD

Ok I calculated A= 0.57 mm is this reasonable?

6. Apr 27, 2014

### KiNGGeexD

I miss calculated,

A= 39.6 cm

7. Apr 27, 2014

### KiNGGeexD

This gives me a max velocity of

1.96 m/s
Which first occurs after 0.317 seconds

8. Apr 27, 2014

### paisiello2

OK, more reasonable.

9. Apr 27, 2014

### KiNGGeexD

Sorry I posted rather to much there which post is that directed to?

10. Apr 27, 2014

### paisiello2

Post #7.

11. Apr 27, 2014

### KiNGGeexD

Those values seem on then??

12. Apr 27, 2014

### KiNGGeexD

Thanks a bunch for all your help