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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
Figure shows the circular motion of a particle. The radius of the circle, the period, sense of revolution and the initial position are indicated in the figure. The simple harmonic motion of the $x-$ projection of the radius vector of the rotating particle $P$ is
Two particles are in $SHM$ in a straight line. Amplitude $A$ and time period $T$ of both the particles are equal. At time $t=0,$ one particle is at displacement $y_1= +A$ and the other at $y_2= -A/2,$ and they are approaching towards each other. After what time they cross each other ?
The scale of a spring balance reading from $0$ to $10 \,kg$ is $0.25\, m$ long. A body suspended from the balance oscillates vertically with a period of $\pi /10$ second. The mass suspended is ..... $kg$ (neglect the mass of the spring)
Due to some force $F_1$ a body oscillates with period $4/5\, sec$ and due to other force $F_2$ oscillates with period $3/5\, sec$. If both forces act simultaneously, the new period will be .... $\sec$
A particle is executing simple harmonic motion $(SHM)$ of amplitude $A,$ along the $x-$ axis, about $x = 0.$ When its potential energy $(PE)$ equals kinetic energy $(KE),$ the position of the particle will be
The velocity of a particle executing SHM varies with displacement $( x )$ as $4 v ^2=50- x ^2$. The time period of oscillations is $\frac{x}{7} s$. The value of $x$ is $............$ $\left(\right.$ Take $\left.\pi=\frac{22}{7}\right)$