NCERT Class 11 Physics Solutions: Chapter 14 – Oscillations-Part 18

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Question 14.25:

A mass attached to a spring is free to oscillate, with angular velocity , in a horizontal plane without friction or damping. It is pulled to a distance and pushed towards the centre with a velocity at time . Determine the amplitude of the resulting oscillations in terms of the parameters [Hint: Start with the equation and note that the initial velocity is negative.]

Answer:

The displacement equation for an oscillating mass is given by:

Where,

is the amplitude

is the displacement

is the phase constant

Velocity,

At,

And,

Squaring and adding equations , we get:

Hence, the amplitude of the resulting oscillation is