A vertical mass-spring system executes simple | vedclass

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

Question

(B) For a simple harmonic oscillator,the displacement is given by $x(t) = A \sin(\omega t)$.The period of oscillation is $T = 2\,s$,so the angular fre

Vedclass · Accepted Answer

Potential energy

Vedclass · Answer

(B) For a simple harmonic oscillator,the displacement is given by $x(t) = A \sin(\omega t)$.The period of oscillation is $T = 2\,s$,so the angular frequency is $\omega = \frac{2\pi}{T} = \pi\,rad/s$.Velocity is $v(t) = A\omega \cos(\omega t)$,which oscillates with the same period $T = 2\,s$.Potential energy is $U = \frac{1}{2} k x^2 = \frac{1}{2} k A^2 \sin^2(\omega t) = \frac{1}{4} k A^2 (1 - \cos(2\omega t))$. This oscillates with a period $T' = \frac{T}{2} = 1\,s$.Kinetic energy is $K = \frac{1}{2} m v^2 = \frac{1}{2} m A^2 \omega^2 \cos^2(\omega t) = \frac{1}{4} m A^2 \omega^2 (1 + \cos(2\omega t))$. This also oscillates with a period $T' = 1\,s$.The difference between kinetic and potential energy is $K - U = \frac{1}{2} m \omega^2 A^2 \cos(2\omega t)$,which oscillates with a period $T' = 1\,s$.However,in standard physics problems of this type,Potential Energy is the classic example of a quantity oscillating at double the frequency (half the period) of the displacement.

$A$ vertical mass-spring system executes simple harmonic oscillations with a period of $2\,s$. $A$ quantity of this system which exhibits simple harmonic variation with a period of $1\,s$ is

Similar Questions

If a polygon of $n$ sides has $275$ diagonals,then $n$ is equal to

Which of the following is the correct order of stability for alkali metal chlorides?

$A$ string is stretched between fixed points separated by $75.0 \ cm$. It is observed to have resonant frequencies of $420 \ Hz$ and $315 \ Hz$. There are no other resonant frequencies between these two. Then,the lowest resonant frequency for this string is .... $Hz$.

The equations of the circle which pass through the origin and make intercepts of lengths $4$ and $8$ on the $x$ and $y$-axes respectively are

$A$ train leaves Pune at $7:30\,am$ and reaches Mumbai at $11:30\,am$. Another train leaves Mumbai at $9:30\,am$ and reaches Pune at $1:00\,pm$. Assuming that the two trains travel at constant speeds,at what time do the two trains cross each other?

Vedclass Test Series

Exam Paper Generator

Online Exam Module