A particle of mass (m) is attached to a spring (of spring constant k) and has a natural angular frequency `omega_(0)`. An external force `F(t)` proportional to `cos omegat` `(omega!=omega_(0))` is applied to the oscillator. The time displacement of the oscillator will be proportional to.

Options

A. `(m)/(omega_(0)^(2) - omega^(2))`
B. `(1)/(m(omega_(0)^(2) - omega^(2)))`
C. `(1)/(m(omega_(0)^(2) + omega^(2)))`
D. `(m)/(omega_(0)^(2) + omega_(2))`

Answer

B

Explanation

Natural frequency of oscillator `= omega_(0)`
Frequency of the applied force `= omega`
Net force acting on oscillator at a displacement `x`
`= m(omega_(0^(2)) - omega^(2))x"….."(i)`
From eqs. (i) and (ii) we get
`m(omega_(0^(2)) - omega^(2)) x prop cosomegat"......."(ii)`
Also `x = Acosomegat"....."(vi)`
From eqs. (iii) and (iv), we get
`m(omega_(0^(2)) - omega^(2))Acosomegat prop cosomegat rArr A prop (1)/(m(omega_(0)^(2) -omega^(2)))`