MEDIUM
Physics
IMPORTANT
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A block of mass m is tied to one end of a spring which passes over a smooth fixed pulley A and under a light smooth movable pulley B. The other end of the string is attached to the lower end of a spring of spring constant K2. Find the period of small oscillation of mass m about its equilibrium position (in second). (Take m=π2 kg,K2=4K1 and K1=17 N/m. )

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Important Questions on Linear and Angular Simple Harmonic Motion

HARD
Physics
IMPORTANT
In the arrangement shown in the given figure, pulleys are small and light, and springs are ideal and K1=25π2 N m-1, K2=2K1K3=3K1 and K4=4K1 are the force constants of the springs. Calculate the period of small vertical oscillations of block of mass m=3 kg.
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MEDIUM
Physics
IMPORTANT

In the figure shown a plate of mass 60 g is at rest and in equilibrium. A particle of mass m=30 g is released from height 4.5mg/k from the plate. The particle sticks to the plate. Neglecting the duration of collision find the time from the collision of the particle and plate to the moment when the spring has maximum compression. Spring has force constant 1 N/m. Calculate the value of time in the form π/x and find the value of x.

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HARD
Physics
IMPORTANT

Two uniform ropes having linear mass densities m and 4 m are joined to form a closed loop. The loop is hanging over a fixed frictionless small pulley with the lighter rope above as shown in the following figure (in the figure equilibrium position is shown). Now if point A (joint) is slightly displaced in downward direction and released, It is found that the loop performs SHM with the period of oscillation equal to N. Find the value of N (take l=150m4π2,g=10 m/s2.

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HARD
Physics
IMPORTANT
A weightless rigid rod with a small iron bob at the end is hinged at point A by a ball and socket joint to the wall so that it can rotate in all directions. The rod is kept in the horizontal position by a vertical inextensible string of length 20 cm, fixed at its midpoint. The bob is displaced slightly, perpendicular to the plane of the figure. If the period of small oscillations of the system is xπ10 s, then what is the value of x? [Take g=10 m s-2]
Picture 171
HARD
Physics
IMPORTANT
A force F=-4 x+8 (in N ) is acting on block where x is the position of block in metres. The energy of oscillation is 32 J. The block oscillates between two points, Out of which value of position of one point (in $\mathrm{m}$ ) is an integer from 0 to 9 . Find it.
MEDIUM
Physics
IMPORTANT
A particle executes SHM along x -axis with a frequency 25π Hz. The mass of a particle is 0.20 kg. At the position x=0.04 m, the kinetic energy is 0.50 J and the potential energy is 0.40 J. The potential energy is zero at mean position. Find the amplitude of oscillations (in cm).
MEDIUM
Physics
IMPORTANT
A particle is moving on X-axis and has potential energy U=2-20x+5x2 joule, where x is position. The particle is released at x=-3. If the mass of the particle is 0.1 kg, then the maximum velocity (in ms-1 ) of the particle is 25β. If amplitude is 5 m, then find the value of β.
HARD
Physics
IMPORTANT

A sphere of mass M and radius R is on a smooth fixed inclined plane in equilibrium as shown in the figure. If now the sphere is displaced through a small distance along the plane, what will be the angular frequency (in rads-1 of the resulting SHM? (Given, k=4M3 )

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