Example 5 A S.H.M. is given by x = 5 sin (3t + f) is to be split into two components such that one leads it by 30⁰ and the other lags it by 80⁰. Find the components.

Solution

Let the required components be given by x₁ = a₁sin ( 3t + f - 80⁰) and x₂ = a₂ sin (3t + f + 30⁰). We can solve the equation graphically as shown in the figure.

Procedure

Example 6 A body is subjected to two S.H.M. as given below x₁ = 15 sin (wt + p/6) and x₂ = 8 cos (wt + p/3) what harmonic motion, should be given to the body to bring it to 'static equilibrium'?

Solution

Index

9.1 The Expression A sin wt + B coswt
9.2 Simple Harmonic Motion

Chapter 1