Question
Question: A particle is executing SHM x = 3 cosωt + 4 sin ωt, Find the phase shift and amplitude....
A particle is executing SHM x = 3 cosωt + 4 sin ωt, Find the phase shift and amplitude.
A
500, 5 units
B
370, 3.5 units
C
530, 3.5 units
D
370, 5 units
Answer
370, 5 units
Explanation
Solution
x = x0 sin
= x0 sin ωt + cosφ + x0cos
ωt sin φ = 3 cos ωt+ 4 sin ωt
Comparing we get x0 cos φ = 4.......(1)
and x0 sin φ = 3 .......(2)
dividing (2) by (1)
tan φ = 3/4 or φ= 370.
Squaring and adding (1) and (2) we get
x0 = 5.