Every question from past board papers on Spring oscillations, restoring force, force constant, newest paper first. Open any question for its full worked answer.
In an oscillating spring mass system, a spring is connected to a box filled with sand. As the box oscillates, sand leaks slowly out of the box vertically so that the average frequency \(\omega(t)\) and average amplitude \(A(t)\) of the system change with time \(t\). Which one of the following options schematically depicts these changes correctly?
A spring is stretched by 5 cm by a force 10 N. The time period of the oscillations when a mass of 2 kg is suspended by it is :
A spring of force constant k is cut into lengths of ratio 1 : 2 : 3. They are connected in series and the new force constant is k'. Then they are connected in parallel and force constant is k''. Then k' : k'' is :
A body of mass \(m\) is attached to the lower end of a spring whose upper end is fixed. The spring has negligible mass. When the mass \(m\) is slightly pulled down and released, it oscillates with a time period of 3 s. When the mass \(m\) is increased by 1 kg, the time period of oscillations becomes 5 s. The value of \(m\) in kg is
