A body of mass 1 kg is executing simple harmonic motion. Its displacement y(c m) at t seconds is given by y=6 sin (100 t+(π/4)). Its maximum kinetic energy is:

Question

A body of mass 1 kg is executing simple harmonic motion. Its displacement y(c m) at t seconds is given by y=6 sin (100 t+(π/4)). Its maximum kinetic energy is: (A) 6 J (B) 18 J (C) 24 J (D) 36 J

Tardigrade Admin · Accepted Answer

y = A sin (ω t +φ) A =6 cm m =1 kg ω=100 rad / sec KE max =(1/2) m ω2 A 2 =(1/2) × 1 ×(100)2 ×(10-2)2 × 62 =18 J

Q. A body of mass $1 k g$ is executing simple harmonic motion. Its displacement $y (c m)$ at $t$ seconds is given by $y = 6 sin (100 t + \frac{π}{4})$ . Its maximum kinetic energy is:

$6 J$

$18 J$

$24 J$

$36 J$

$y = A sin (ω t + ϕ)$
$A = 6 c m$
$m = 1 k g$
$ω = 100 r a d / sec$
$K E_{m a x} = \frac{1}{2} m ω^{2} A^{2}$
$= \frac{1}{2} \times 1 \times (100)^{2} \times (1 0^{- 2})^{2} \times 6^{2}$
$= 18 J$

Q. A body of mass 1kg is executing simple harmonic motion. Its displacement y(cm) at t seconds is given by y=6sin(100t+4π​). Its maximum kinetic energy is:

6J

18J

24J

36J