A particle doing simple harmonic motion, amplitude $$=$$ $$4$$ cm, time period $$=$$ $$12$$ $$sec$$. The ratio between time taken by it in going from its mean position to $$2$$ cm and from $$2$$ cm to extreme position is

Question

Infinity Learn · Accepted Answer

ω $$=$$ $$2$$$$π$$T $$=$$ $$2$$$$π$$$$12$$ $$=$$ π $$rad6$$ $$sec$$(For$$ y $$=$$ $$2$$ $$cm) $$2$$ $$=$$ $$4($$$$sin$$ π$$6t1)By$$ solving $$t1$$ $$=$$ $$1$$ $$sec$$ (For$$ y $$=$$ $$4$$ $$cm) $$t2$$ $$=$$ $$3$$ $$sec$$ So time taken by particle in going from $$2$$ cm to extreme position is $$t2-t1$$ $$=$$ $$2$$ $$sec$$. Hence required ratio will be $$12$$

A particle doing simple harmonic motion, amplitude = 4 cm, time period = 12 sec. The ratio between time taken by it in going from its mean position to 2 cm and from 2 cm to extreme position is

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