A body executing simple harmonic motion has a maximum acceleration equal to $ 24\,metres/se{c^2} $ and maximum velocity equal to $ 16\;metres/sec $. The amplitude of the simple harmonic motion is
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Two particles execute $SHM$ of same amplitude of $20\, cm$ with same period along the same line about the same equilibrium position. The maximum distance between the two is $20\, cm.$ Their phase difference in radians is
Time period of a simple pendulum is $T$. The time taken to complete $5 / 8$ oscillations starting from mean position is $\frac{\alpha}{\beta} T$. The value of $\alpha$ is ..... .
The variation of displacement with time of a particle executing free simple harmonic motion is shown in the figure. The potential energy ${U}({x})$ versus time $({t})$ plot of the particle is correctly shown in figure:
A mass $m =100\, gms$ is attached at the end of a light spring which oscillates on a frictionless horizontal table with an amplitude equal to $0.16$ metre and time period equal to $2 \,sec$. Initially the mass is released from rest at $t = 0$ and displacement $x = - 0.16$ metre. The expression for the displacement of the mass at any time $t$ is
The metallic bob of simple pendulum has the relative density $5$. The time period of this pendulum is $10\,s$. If the metallic bob is immersed in water, then the new time period becomes $5 \sqrt{ x } s$. The value of $x$ will be.
The displacement of a particle executing periodic motion is given by :
$y = 4cos^2\,(t/2)sin\,(1000t)$
This expression may be considered to be a result of superposition of
On a frictionless horizontal plane, a bob of mass $m=0.1 kg$ is attached to a spring with natural length $l_0=0.1 m$. The spring constant is $k_1=0.009 Nm ^{-1}$ when the length of the spring $I > l_0$ and is $k_2=0.016 Nm ^{-1}$ when $ I < l_0$. Initially the bob is released from $l=0.15 m$. Assume that Hooke's law remains valid throughout the motion. If the time period of the full oscillation is $T=(n \pi) s$, then the integer closest to $n$ is. . . . .
A particle executes $SHM$ with amplitude of $20 \,cm$ and time period is $12\, sec$. What is the minimum time required for it to move between two points $10\, cm$ on either side of the mean position ..... $\sec$ ?