# Oscillating mechanical systems. find maximum velocity and acceleration ?

1. Sep 25, 2011

### bensm0

Oscillating mechanical systems. find maximum velocity and acceleration !?

A mass of 0.3 kg is suspended from a spring of stiffness 200 N m–1. If the mass is displaced by 10 mm from its equilibrium position and released, for the resulting vibration

A) Calculate maximum velocity
B) Calculate maximum acceleration

I need help with this please, for starters is the amplitude 0.01m?

Thanks

2. Sep 25, 2011

### lewando

Re: Oscillating mechanical systems. find maximum velocity and acceleration !?

Yes, amplitude is correct, you must have had some training . Welcome to PF. There are a ton of googleable resources out there. Check them out, give the problem a try and come back with some specific questions.

3. Sep 26, 2011

### bensm0

Re: Oscillating mechanical systems. find maximum velocity and acceleration !?

Ok thanks

I think i've got it now

using:-

v=- ωA sin(ωt - φ)
a= - ω2A cos(ωt - φ)

And the maximums occur when sin(ωt - φ)=1 and cos(ωt - φ)=1

Thanks again!

4. Sep 26, 2011

### rude man

Re: Oscillating mechanical systems. find maximum velocity and acceleration !?

5. Sep 27, 2011

### bensm0

Re: Oscillating mechanical systems. find maximum velocity and acceleration !?

omega = square root (k/m) = 25.82

a) 0.001 x 25.82 x 1 = 0.2582 m/s

b)0.001 x 25.82^2 x 1 = 6.6667 m/s^2

Anybody care to have a go at the last question:-

d) the mass required to produce double the maximum velocity
calculated in (b) using the same spring and initial deflection

I get an answer of 0.075kg

Thanks

6. Mar 12, 2013

### eddievic

would this not be 0.15kg?

ω = √k/m = 200/0.15 = 36.51

b)0.001 x 36.51^2 x 1 = 13.33 m/s^2 = double Vmax

I know this is a late response to a question but i have the same question and want to check my working.

7. Mar 27, 2013

Eddievic,

I got the same answers as bensm0,

If you double the answer that you got in a) 0.5164
use that in your equasions and transpose for mass.

i think :)

8. Apr 3, 2013

### eddievic

I believe you are correct my paper came back and mine was incorrect the paper was an overall pass though so I have not investigated it fully.