The springs shown in the figure are all unstretched in the beginning when a man starts pulling the blook. The man exerts a constant force F on the block. Find the amplitude and the frequency of the motion of the block.

The springs shown in the figure are all unstretched in the beginning w

1.	The springs shown in the figure are all unstretched in the beginning when a man starts pulling the blook. The man exerts a constant force F on the block. Find the amplitude and the frequency of the motion of the block.
Answer» Solution :In this CASE `k_2 , k_3` are in series RESULTING a force CONSTANT `(k_2 k_3)/(k_2 + k_3)` To this `k_1` is in parallel So, effective spring constant is `(k_2 k_3)/(k_2 + k_3) + k_1 = (k_1 k_2 + k_2 K_3 + K_3 k_1)/(k_2 + k_3)` From the previous problem amplitude of oscillation = `F/k` So `A= (F(k_2 + k_3))/(k_1 k_2 + k_2 k_3 + k_3 k_1)` Frequence of oscillation `f= 1/(2pi) SQRT((k)/(m)) = 1/(2pi) sqrt((k_1 k_2 + k_2 k_3 + k_3 k_1)/(m(k_2 + k_3)))`