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  • Which of the following statements is/are true for a simple hannonic oscillator? (a) Force acting is directly proportional to displacement from the mean position and opposite to it

Which of the following statements is/are true for a simple hannonic oscillator?
(a) Force acting is directly proportional to displacement from the mean position and opposite to it
(b) Motion is periodic
(c) Acceleration of the oscillator is constant
(d) The velocity is periodic

Answers (1)

The answer is the option (a) Force acting is directly proportional to the displacement from the mean position and opposite to it, (b) Motion is periodic, and (d) The velocity is periodic.

Explanation: Let, x = a \sin \omega t, be a SHM   …… (i)

V = \frac{dx}{dt} = \alpha \omega \cos \omega …. (ii)

V = \frac{dv}{dt} = \alpha \omega\left ( - \omega \sin \omega t \right )

Thus, A = - \alpha \omega ^{2} \sin \omega t  or A = -ω2x

mA = -m\omega ^{2}x

Hence, F \propto (-x)

Now, x(t) = x(t + T)

Thus, the motion is periodic and simple harmonic.

Now, from (ii),

v(t) = v(t + T)

Hence, opt, (a), (b) & (d) are correct options.

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