
A block of mass is tied to one end of a spring which passes over a smooth fixed pulley and under a light smooth movable pulley . The other end of the string is attached to the lower end of a spring of spring constant . Find the period of small oscillation of mass about its equilibrium position (in second). (Take and )


Important Questions on Linear and Angular Simple Harmonic Motion


In the figure shown a plate of mass is at rest and in equilibrium. A particle of mass is released from height 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 . Calculate the value of time in the form and find the value of .

Two uniform ropes having linear mass densities and 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 (joint) is slightly displaced in downward direction and released, It is found that the loop performs SHM with the period of oscillation equal to . Find the value of (take





A sphere of mass and radius 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 of the resulting SHM? (Given, )
