Question

The strings shown in the figure are all unattached in the begining when a man starts pulling the block. find the amplitude and frequency of the motion of the block .​

Answer 1

The springs shown in the figure (12-E7) are all unstretched in the beginning when a man starts pulling the block. The man exerts a constant force F on the block. Find the amplitude and the frequency of the motion of the block. Read more on Sarthaks.com - https://www.sarthaks.com/43295/springs-shown-the-figure-are-all-unstretched-the-beginning-when-man-starts-pulling-block

Answer 2

Solution :- k2 and k3 are in series .

Let equivalent spring constant to be k4

•°• 1/k4 = 1/k2 + 1/k3

k4 = k2* k3/k2 + k3

now , k4 and k1 are in parallel .

so , equivalent spring constant K = k1 + k4 = k1+ k2*k3 /k2 + k3

k = k1*k2 + k1*k3 + k2*k3/k2+k3

$t = 2\pi \sqrt{ \frac{m}{k} }$

$t \: = 2\pi \sqrt{ \frac{m(k2 + k3)}{k2k3 +k1k2 + k1k3 } }$


(b) frequency = 1/T = 1/2π √k2k3+k1k2 + k1 k3/M(k2+k3)

(c) Amplitude, x = f/k

= F ( k2 + k3)/k1k2 + k2k3 + k1 k3 .