An object of mass 0.5, text{kg} is executing | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Given: Mass $m = 0.5\, 	ext{kg}$,Amplitude $A = 5\, 	ext{cm} = 0.05\, 	ext{m}$,Time period $T = 0.2\, 	ext{s}$.First,calculate the force const

Vedclass · Accepted Answer

$0.625$

Vedclass · Answer

(B) Given: Mass $m = 0.5\, 	ext{kg}$,Amplitude $A = 5\, 	ext{cm} = 0.05\, 	ext{m}$,Time period $T = 0.2\, 	ext{s}$.First,calculate the force constant $k$ using the formula $T = 2\pi \sqrt{\frac{m}{k}}$:$0.2 = 2\pi \sqrt{\frac{0.5}{k}}$$0.1 = \pi \sqrt{\frac{0.5}{k}}$$0.01 = \pi^2 \left(\frac{0.5}{k}ight)$$k = \frac{0.5 \pi^2}{0.01} = 50 \pi^2 \approx 50 	imes 9.87 = 493.5\, 	ext{N/m}$.Next,find the displacement $x$ at $t = \frac{T}{4}$ starting from the mean position $(\phi = 0)$:$x = A \sin(\omega t) = A \sin\left(\frac{2\pi}{T} \cdot \frac{T}{4}ight) = A \sin\left(\frac{\pi}{2}ight) = A = 0.05\, 	ext{m}$.Now,calculate the potential energy $PE$:$PE = \frac{1}{2} k x^2 = \frac{1}{2} 	imes (50 \pi^2) 	imes (0.05)^2$$PE = 25 \pi^2 	imes 0.0025 = 0.0625 \pi^2 \approx 0.0625 	imes 9.87 \approx 0.617\, 	ext{J}$.Rounding to the nearest provided option,we get $0.625\, 	ext{J}$.

Similar Questions

The potential energy of a simple harmonic oscillator of mass $2\, kg$ in its mean position is $5\, J.$ If its total energy is $9\, J$ and its amplitude is $0.01\, m,$ its time period would be

$A$ body is performing simple harmonic motion with an amplitude of $10 \, cm$. The velocity of the body is tripled by an air jet when it is at $5 \, cm$ from its mean position. The new amplitude of vibration is $\sqrt{x} \, cm$. The value of $x$ is . . . . . . .

The total energy of a simple harmonic oscillator is $E$. What is its kinetic energy at half the amplitude?

The total energy of a particle executing $SHM$ at an amplitude of $4 \, cm$ is $20 \, J$. What will be its total energy at a displacement of $x = 2 \, cm$ (in $J$)?

When a longitudinal wave propagates through a medium,the particles of the medium execute simple harmonic oscillations about their mean positions. These oscillations of a particle are characterised by an invariant

Vedclass Test Series

Exam Paper Generator

Online Exam Module