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A particle is undergoing SHM with amplitude 10cm. The maximum speed it achieves is 1m/s. Find the time it takes to reach from the mean position to half the amplitude.(a) π/60 s(b) π/30 s(c) π/15 s(d) π/40 sI got this question by my college director while I was bunking the class.This is a very interesting question from Simple Harmonic Motion in portion Oscillations of Physics – Class 11

Answer»

Right ANSWER is (a) π/60 s

The best explanation: LET the equation of motion be: x = 0.1sin(wt) where w is the angular frequency.

On derivating this equation w.r.t time we get: v = 0.1wcos(wt).

Given that MAXIMUM speed is 1m/s, we get 0.1w = 1.

∴ w = 10s^-1.

Now our equation of motion has become: x = 0.1sin(10t).

Assume we start from x=0 at t=0.Then by PUTTING x=0.05 in the equation we can find the time.0.05 = 0.1 sin(10t)∴ sin(10t) = 0.5∴ 10t = π/6∴ t = π/60 s.



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