Question

Two springs of force constant K and 2K are connected to a mass as shown below the frequency of oscillation of the mass is

Answer 1

Answer:

Let the mass m be displaced toward right by a distance x. Then, spring 1 will be extended and the spring 2 will be compressed by en amount x. On releasing mass m the restoring force on m due to spring 1 is F1=−kx and restoring force due to spring 2 is F2=−2kx

 Total restoring force on mass m is

F=F1+F2

F=−kx−2kx=−3kx

F=dt2md2x=−3kx

dt2d2x=−m3kx

dt2d2x+m3kx=0

This is similar to dt2d2x+ω2x=0

Which respresent equation of SHM. Comparing the two equations, ω2=m3k

ω=m3k

2πf=m3k

f=2π1m3k