The displacement of particle performing simple harmonic motion is given by, x = 8 sin wt + 6 cos wt, - Physics - Magnetism And Matter

Question

The displacement of particle performing simple harmonic motion is
given by, x = 8 sin wt + 6 cos wt, where distance is in cm and time
is in second The amplitude of motion is
(a) 10 cm (b) 14 cm (c) 2 cm (d) 3 5 cm

Deepak Kumar · Accepted Answer

Dear Student ,The amplitude is a maximum displacement from the mean position
 So here SHM is given x=8sin ωt+6cos ωt Here phase difference is δ=90o ,cos 90o=0now  a1= 8 , a2=6 So amplitude of the motion =(a12+a22+2a1a2cosδ)                                             =(64+36)                                         = 100                                         = 10cmSo option (1) is correct 
 Regards

The displacement of particle performing simple harmonic motion is given by, x = 8 sin wt + 6 cos wt, where distance is in cm and time is in second. The amplitude of motion is (a) 10 cm (b) 14 cm (c) 2 cm (d) 3.5 cm

The displacement of particle performing simple harmonic motion is given by, x = 8 sin wt + 6 cos wt, where distance is in cm and time is in second. The amplitude of motion is
(a) 10 cm (b) 14 cm (c) 2 cm (d) 3.5 cm