Problem #0103 Mechanics Sub-menu Problem #0105 Chapters Chapters

104.

Problem 15.21(RHK)

Two springs are attached to a block of mass m, free to slide on a frictionless horizontal surface. We have to show that the frequency of oscillation of the block is

where and are the frequencies at which the block would oscillate if connected only to spring 1 or spring 2.

Solution:             Click For PDF Version

Let the block of mass, m, at some instant, be displaced to from its equilibrium position to the right by distance x. Spring with spring-constant in this situation will be stretched and will therefore exert restoring force x on the block in the direction right-to-left, and the spring with spring-constant will be compressed and will exert force x on the block, also, in the direction right-to-left in order to bring the block to its undisturbed position. Therefore, the force due to the combined action of the two springs will be

.

Equation of motion of the block is

It is an equation of SHM. Frequency of this SHM is