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#1 2013-11-28 09:34:44

Registered: 2013-04-13
Posts: 105

Differential equations-exercise

Prove that moving mass m underlying the action of linear spring constant k, has the form y (t) = Asin (wt + f), where t is time and A, w, f fixed. Interpret the physical significance of these constants and determine their values if at the time t = 0, the mass is removed y0 and velocity v0. If in addition the mass subject to outdoor force F (t) = F_ {0} sin (w_ {0} t), amplitude F_ {0} and cyclic frequency w_ {0}, calculate the amplitude of motion and investigate the dependence of the circular frequency w_ {0}.

Could you give me a hint,what I have to do??


#2 2013-11-28 20:07:38

bob bundy
Registered: 2010-06-20
Posts: 8,354

Re: Differential equations-exercise

hi evinda

This is an example of simple harmonic motion.  The basic equation for this is:

The restoring force in the spring will act in a direction that is opposite to the distance y (for extension of the spring) so that's where the minus comes in and omega will depend on the spring constant.

Then you re-write this as

Once you've got that integrated you have to change v into dy/dt and integrate again to get the sine expression.  That's a lot to take in in one go so have a look at what I've said so far and either ask for more detail if something isn't clear or tell me your equation for v, if it is clear.

Then we'll finish the task with the second integration.  smile


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