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Re: Differential equations-exercise
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.
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