Question

the displacement of a particle in shm is x equal to 3 sin (20πt)+4cos(20πt) cm its amplitude of oscillation is

Answer 1

y = x(t) => 'y' is a sinusoidal function of 't'

Let 'm' = wt

--> x(t) = 3 sin m + 4 cos m

= 5 ( 3/5 sin m + 4/5 cos m )

= 5 sin ( m + arctan ( 4/3 ) )

= 5 sin ( wt + arctan ( 4/3 ) )

At 't' = 0 -->

--> x(m) = 5 sin( arctan (4/3) )

= 5 ( 0.8 ) = 4 ✓✓

=> Amplitude of SHM = 4 ✓✓

Hope this helps ^_