An object of mass 0.5 kg is executing simple harmonic motion. It amplitude is 5 cm and time period ( T ) is 0.2 s. What will be the potential energy of the object at an instant t=(T/4) s starting from mean position. Assume that the initial phase of the oscillation is zero.

Question

An object of mass 0.5 kg is executing simple harmonic motion. It amplitude is 5 cm and time period ( T ) is 0.2 s. What will be the potential energy of the object at an instant t=(T/4) s starting from mean position. Assume that the initial phase of the oscillation is zero. (A) 0.62 J (B) 6.2 × 10-3 J (C) 1.2 × 103 J (D) 6.2 × 103 J

Tardigrade Admin · Accepted Answer

T=2 π √(m/k) 0.2=2 π √(0.5/k) k=50 π2 ≈ 500 x=A sin (ω t+φ) =5 cm sin ((ω T/4)+0) =5 cm sin ((π/2)) =5 cm P E=(1/2) k x2 =(1/2)(500)((5/100))2 =0.6255

Q. An object of mass $0.5 k g$ is executing simple harmonic motion. It amplitude is $5 c m$ and time period $(T)$ is $0.2 s$ . What will be the potential energy of the object at an instant $t = \frac{T}{4} s$ starting from mean position. Assume that the initial phase of the oscillation is zero.

$0.62 J$

$6.2 \times 1 0^{- 3} J$

$1.2 \times 1 0^{3} J$

$6.2 \times 1 0^{3} J$

$T = 2 π \frac{m}{k}$
$0.2 = 2 π \frac{0.5}{k}$
$k = 50 π^{2}$
$\approx 500$
$x = A sin (ω t + ϕ)$
$= 5 c m sin (\frac{ω T}{4} + 0)$
$= 5 c m sin (\frac{π}{2})$
$= 5 c m$
$PE = \frac{1}{2} k x^{2}$
$= \frac{1}{2} (500) (\frac{5}{100})^{2}$
$= 0.6255$

Q. An object of mass 0.5kg is executing simple harmonic motion. It amplitude is 5cm and time period (T) is 0.2s. What will be the potential energy of the object at an instant t=4T​s starting from mean position. Assume that the initial phase of the oscillation is zero.

0.62J

6.2×10−3J

1.2×103J

6.2×103J