A particle of mass m is released from rest an | vedclass

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

Question

(A) The potential energy $V(x)$ is given by a parabolic curve,which implies $V(x) = \frac{1}{2}kx^2$. This represents a simple harmonic oscillator whe

Vedclass · Accepted Answer

Vedclass · Answer

(A) The potential energy $V(x)$ is given by a parabolic curve,which implies $V(x) = \frac{1}{2}kx^2$. This represents a simple harmonic oscillator where the restoring force is $F = -\frac{dV}{dx} = -kx$. Since the particle is released from rest at some positive displacement $x = A$ at $t = 0$,its motion is described by the equation $x(t) = A \cos(\omega t)$. At $t = 0$,$x = A$,which is the positive extreme position. As time increases,the particle moves towards the mean position $(x = 0)$ and then to the negative extreme position $(x = -A)$. This behavior is represented by a cosine graph starting from a positive maximum value at $t = 0$.

$A$ particle of mass $m$ is released from rest and follows a parabolic path as shown. Assuming that the displacement of the mass from the origin is small,which graph correctly depicts the position of the particle as a function of time $?$

Similar Questions

$A$ body oscillates with $SHM$ according to the equation (in $SI$ units):
$x = 5 \cos (2 \pi t + \pi / 4)$
At $t = 1.5 \, s$,calculate the:
$(a)$ displacement
$(b)$ speed
$(c)$ acceleration of the body.

$A$ particle executes simple harmonic motion according to the equation $x(t) = A \sin^2(\alpha t)$. If the time period of the $SHM$ is $0.2 \ s$, then the value of $\alpha$ (in units of $rad/s$) is (in $\pi$)

What is constant in $S.H.M.$?

What is periodic motion? Give its examples.

The displacement of a particle performing linear $S.H.M.$ is given by $y = A \cos[\pi(t + \phi)]$. If at $t = 0$, the displacement is $y = 2 \text{ cm}$ and velocity is $2\pi \text{ cm/s}$, the value of amplitude $A$ in $\text{cm}$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module