Q: The mass M shown in the figure oscillates in simple harmonic motion with amplitude A. The amplitude of the point P is

(a) $ \displaystyle \frac{k_1 A}{k_2} $

(b) $ \displaystyle \frac{k_2 A}{k_1} $

(c) $ \displaystyle \frac{k_1 A}{k_1 + k_2} $

(d) $ \displaystyle \frac{k_2 A}{k_1 + k_2} $

Ans: (d)

Sol: When two springs are in series, the tension or force is the same for both. Therefore,

k_{1} x_{1} = k_{2} x_{2}

x_{2} = k_{1} x_{1} / k_{2}

Total extension (i.e.,amplitude)= sum of the extensions x_{1} and x_{2}

A = x_{1} + x_{2}

A = x_{1} + (k_{1} x_{1} )/ k_{2}

x_{1} = k_{2} A/(k_{1} + k_{2})