Question
A particle of mass m is attached to a spring (of spring constant k) and has a natural angular frequency ω0. An external force F(t) proportional to cosωt (ω≠ω0) is applied to the oscillator. The time displacement of the oscillator will be proportional to
Solution
B.
Initial angular velocity of particle = ω0 and at any instant t, angular velocity = ω Therefore, for a displacement x, the resultant acceleration
Now, equation of simple harmonic motion
x = A sin (ωt + φ) .......... (iv)
at t = 0 ; x = A
∴ A = A sin( 0 + φ )
⇒ φ =π/2
..........(v)
Hence, from equations (iii) and (v), we finally get
