Physics Oscillations

For an SHM oscillator, the amplitude is 5 cm and its time period is 4 seconds. The minimum time taken by the particle to pass between points which are at distances 4 cm and 3 cm from the centre of oscillation on the same side of it will be

If we want that a simple pendulum oscillates with same time period in summer as it did in winter, what changes to the simple pendulum should we do during summer?

A rod is clamped at both of its ends and stationary longitudinal waves are produced in it. In first experiment, the rod has a total of 4 nodes with amplitude of each anti-node to be 1mm. In other experiment, the rod has a total of 6 nodes with amplitude of each anti node to be 2mm. The energy of vibrations in the rod in two case is E₁ and E₂ respectively. Write value of  

Two particles are executing SHM which are described by the equations x₁ = asin(ωt + π/6) and x₂ = asin(ωt + π/4). Find the minimum time interval between the particles to cross their mean position.

A string of mass per unit length $\mu$  is clamped at both ends such that one end of the string is at x = 0 and the other end at x = L. When string vibrates in fundamental mode, amplitude of the midpoint of string is a and tension is string is F. Find the total oscillation energy (in J) stored in the string.

(Use L = 1m, F = 10 N, a =   $\frac{1}{\pi }m)$

A solid cylinder attached to horizontal massless spring can roll without slipping along horizontal surface. Find time period of oscillation.

A block ' $A$ ' of mass $m$ attached to a massless spring is performing oscillatory motion of amplitude ' $A$ ' on a frictionless horizontal plane. If it collides elastically with another block ' $\mathrm{B}$ ' of mass $2\mathrm{m}$ kept initially at rest, when ' $\mathrm{A}$ ' is passing through its equilibrium point, the amplitude of oscillation for the block ' $\mathrm{A}$ ' become $f$ A. The value of $f$  is:

The fundamental frequency of an organ pipe open at one end is 300 Hz. The frequency of 3rd overtone of n Find n.*this organ pipe is 100 Hz

The first overtone frequency of an open organ pipe is equal to the fundamental frequency of a closed organ pipe. If the length of the closed organ pipe is 20cm. The length of the open organ pipe is……….cm.

In the given figure, a mass M is attached to a horizontal spring which is fixed on one side to a rigid support. The spring constant of the spring is k. The mass oscillates on a frictionless surface with time period T and amplitude A. When the mass is in equilibrium position, as shown in the figure, another mass m is gently fixed upon it. New amplitude of oscillation will be: