Question

Find the natural frequency of oscillation of the system as shown in figure. Pulleys are massless and frictionless. Spring and string are also massless.

• A. $\frac{\pi }{2}$
• B. $\sqrt{\pi }$
• C. $\sqrt{\frac{10}{\pi }}$
• D. $\pi$

Answer 1

Answer: (D)

$\pi$

X is distance

F mass extended by lower pulley

string of lower pulley $F/2$

contributed hakf of spring $F/4$

mass goes down by x and lower pulley X

upper pullley 2x

spring stretch 4x

$K\times 4x=F/4=F=16kx$

$-16kx/m=-(16\times 25/1)x=400x$

$\omega =\sqrt{400}=20rad/s$

$f=\frac{\omega }{2\pi }=20/\left(2\pi \right)=10/\pi =\pi Hz$