Question

A mass m. lying on a horizontal frictionless
surface, is connected to one end of a spring.
The other end of the spring is connected to a
Wall, as shown in the figure. At t=0, the
mass is given an impulse
•
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The time dependence of
the displacement and the velocity of the mass (in terms of non-zero
constants A and B) are

given by

(a) x(t) = Asinwt , v(t) = B coswt
(b) x(t) = Asin wt, v(t) = B sinwt
(c) x(t)= A cos wt, v(t) = B sinwt.
(d) x(t) = A coswt, v(t) = B cos wt​

Answer 1

Explanation:

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(a) x(t) = Asinwt , v(t) = B coswt

Answer 2

The time dependence of the displacement and the velocity of the mass (in terms of non-zero constants A and B are given by (c) x(t)= A cos wt, v(t) = B sinwt.

• A mass attached to spring when given an impulse starts oscillating to and fro.
• These oscillations are simple harmonic motions.
• Since the motion of the block is starting from the amplitude of the SHM, the equation of displacement will be x(t)= A cos wt.
• The phase difference between the displacement and the velocity equation for SHM is π/2 so the equation of velocity will be v(t)= B sinwt.