A particle is executing simple harmonic motion with a time period $T.$ At time $t = 0$, it is at its position of equilibrium. The kinetic energy-time graph of the particle will look like
JEE MAIN 2017, Medium
Download our app for free and get started
For a particle executing $SHM$
At mean position; $t=0, \omega t=0, y=0, V=V_{\max }=a \omega$
$K . E .=K E_{\max }=\frac{1}{2} m \omega^{2} a^{2}$
At extreme position $: t=\frac{T}{4}, \omega t=\frac{\pi}{2}, y=A, V=V_{\min }=0$
$\therefore \quad K . E .=K E_{\min }=0$
Kinetic energy in $S H M, K E=\frac{1}{2} m \omega^{2}\left(a^{2}-y^{2}\right)$
$=\frac{1}{2} m \omega^{2} a^{2} \cos ^{2} \omega t$
Download our appand get started for free
Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*
Similar Questions
- 1The potential energy of a particle $\left(U_x\right)$ executing $S.H.M$. is given byView Solution
- 2On a planet a freely falling body takes $2 \,sec$ when it is dropped from a height of $8 \,m$, the time period of simple pendulum of length $1\, m$ on that planet is ..... $\sec$View Solution
- 3A particle executes $S.H.M.$ and its position varies with time as $x=A$ sin $\omega t$. Its average speed during its motion from mean position to mid-point of mean and extreme position isView Solution
- 4The motion of a simple pendulum excuting $S.H.M$. is represented by following equation.View Solution
$Y = A \sin (\pi t +\phi)$, where time is measured in $second$.
The length of pendulum is .............$cm$
- 5A particle of mass $m$ undergoes oscillations about $x=0$ in a potential given by $V(x)-\frac{1}{2} k x^2-V_0 \cos \left(\frac{x}{a}\right)$, where $V_0, k, a$ are constants. If the amplitude of oscillation is much smaller than $a$, the time period is given byView Solution
- 6A particle moves in space according to equationView Solution
$\vec r = (\sin \,t\,\hat i\, + \,\cos \,t\,\hat j\, + \,t\,\hat k)m$
Find time $'t'$ when position vector and acceleration vector are perpendicular to each other
- 7Block $A$ is hanging from a vertical spring and it is at rest. Block $'B'$ strikes the block $'A'$ with velocity $v$ and stick to it. Then the velocity $v$ for which the spring just attains natural length is:View Solution
- 8Two $SHM$ are represented by equations, $y_1 = 6\cos \left( {6\pi t + \frac{\pi }{6}} \right)\,,{y_2} = 3\left( {\sqrt 3 \sin 3\pi t + \cos 3\pi t} \right)$View Solution
- 9If $x=5 \sin \left(\pi t+\frac{\pi}{3}\right) \mathrm{m}$ represents the motion of a particle executing simple harmonic motion, the amplitude and time period of motion, respectively, areView Solution
- 10The potential energy of a simple harmonic oscillator at mean position is $2\,joules$. If its mean $K.E.$ is $4\,joules$, its total energy will be .... $J$View Solution