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Simple harmonic motion -- manipulating SHM equations

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PeroK

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Thanks all who reply :) Managed to solve this with @Delta2 explanation actually :woot: Answer is ##\frac {2}{\sqrt 3}v##
I don't see how you can work a problem like this without labelling some specific times. After looking at the equations, the first thing I would do is:

Let ##t_0, t_1## be times when the displacement is zero and half the amplitude respectively.

Then you have ##D(t_0) = 0 \ \Rightarrow \ \sin(wt_0) = 0##

Also, strictly speaking, you should be dealing with the absolute value for the speed. Alternatively, you could make a simplifying assumption that the displacements and velocities are positive, hence the sines and cosines are positive, at ##t_0, t_1##.
 

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