Questions in Oscillations

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The vertical extension in a light spring by a weight of 1 kg suspended from the wire is 9.8 cm. The period of oscillation
A particle of mass 200 gm executes S.H.M. The restoring force is provided by a spring of force constant 80 N / m. The time period of oscillations is
The length of a spring is $l$ and its force constant is $k$. When a weight $W$ is suspended from it, its length increases by $x$. If the spring is cut into two equal parts and put in parallel and the same weight $W$ is suspended from them, then the extension will be
A block is placed on a frictionless horizontal table. The mass of the block is m and springs are attached on either side with force constants ${{K}_{1}}$ and ${{K}_{2}}$. If the block is displaced a little and left to oscillate, then the angular frequency of oscillation will be
A uniform spring of force constant k is cut into two pieces, the lengths of which are in the ratio 1 : 2. The ratio of the force constants of the shorter and the longer pieces is
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
A block of mass $m$, attached to a spring of spring constant $k$, oscillates on a smooth horizontal table. The other end of the spring is fixed to a wall. The block has a speed $v$ when the spring is at its natural length. Before coming to an instantaneous rest, if the block moves a distance $x$ from the mean position, then
The force constants of two springs are ${{K}_{1}}$ and ${{K}_{2}}$. Both are stretched till their elastic energies are equal. If the stretching forces are ${{F}_{1}}$ and ${{F}_{2}}$, then ${{F}_{1}}:{{F}_{2}}$ is
A mass $m$ is vertically suspended from a spring of negligible mass; the system oscillates with a frequency $n$. What will be the frequency of the system if a mass $4 m$ is suspended from the same spring
If the period of oscillation of mass m suspended from a spring is 2 sec, then the period of mass 4m will be

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