A cam displaces its follower by 20 mm through simple harmonic motion (SHM). The cam is rotating at 15 RPM and its angle of rise is 90°. The time period of the SHM will be

Question

Question

This question was previously asked in

BPSC AE Paper 6 (Mechanical) 2019 Official Paper

Answer 1

Explanation:

Cam is a mechanical element which is used to deliver the reciprocating or oscillating motion to another machine element known as a follower.
A simple harmonic motion of constant amplitude in which the acceleration is proportional and oppositely directed to the displacement of the body from a position of equilibrium.
A simple harmonic motion curve is widely used since it is simple to design. The curve is the projection of a circle about the cam rotation axis as shown in the figure.

where H = maximum height of follower in SHM motion

Calculation:

Given:

Displacement of follower in SHM = 20 mm, angle of rise θ = 90^o = π /2, speed of cam rotation N = 15 RPM,

Angular velocity of cam ω =

Now time period of the cam in SHM,

T = angle of rise in radian / angular velocity

T = 1 sec

Key Points

The time period in SHM is simply angle turned upon angular velocity.