Question

A harmonic motion is given by x(t)=10sin(30t−π/3) mm. where t is in second and phase angle is in radian. what will be the time period of motion? 1.209 second 0.209 second 0.409 second 0.902 second

Answer 1

equation of SHM is x(t) = 10sin(30t - π/3)
we know, standard form of equation is x(t) = Asin(2πt/T ± Ф)
where A is amplitude ,
T is time period of SHM
Ф is phase constant

Now, compare both equations
we get , 30 = 2π/T
⇒T = 2π/30 = 2 × 22/7 /30 = 44/210 = 0.209 sec

Hence time period of motion is 0.209 second