Question

The timeperiod of the motion u" +192u = 0 is
a) T = 0.45345 b) T = 0.5345 c) T = 0.54345 d) T = 0.345​

Answer 1

The time period of the motion u" + 192 u = 0 is a) T = 0.45345 sec.

Step-by-step explanation:

The given equation is second order ordinary differential equation of angular motion.

u" + 192 u = 0 ⇒ dω²/dt² + α² dω/dt = 0

ω = Angular distance

α = Angular frequency/Angular speed

α = 2π/T

Where,

T = Time period

Now, the angular frequency formula becomes,

α² = (2π/T)²

192 = (2π/T)²

2π/T = √192

2π/T = 13.85

T = 2π/13.85

∴ T = 0.45365 seconds