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,
k1 x1 = k2 x2
x2 = k1 x1 / k2
Total extension (i.e.,amplitude)= sum of the extensions x1 and x2
A = x1 + x2
A = x1 + (k1 x1 )/ k2
x1 = k2 A/(k1 + k2)