When the mass is displaced a little to one side, one spring gets compressed and another is elongated.Due to which the combination of sp[rings. Here, effective spring factor k will be given by \(k={ k }_{ 1 }+{ k }_{ 2 }=600+600=1200{ Nm }^{ -1 }\)

The motion of a simple pendulum is approximately simple harmonic for small angle oscillations. For larger angles of oscillation, a more involved analysis sjows that T is greater than \(2\pi \sqrt { \frac { l }{ g } } \) .Think of a qualitative argument to appreciate this result.

Let us take the position of mass when the spring is unstretched as x = 0 and the direction from left to right as the positive direction of the x-axis. Given x as a function of time t for the oscillating mass, if at the moment we start the stopwatch (t = 0), the mass is at the maximum stretched position.
In what way do these functions for SHM differ from each other, in frequency, in amplitude or the initial phase?

A body weighing 10 g has a velocity of 6 cms^-1 after one second of its starting from mean position. If the time period is 6 s, then find the kinetic energy, potential energy and the total energy.

A girl is swinging in the sitting position. How will the period of the swing be changed if she stands up?

A particle of mass 0.8 kg is executing simple harmonic motion with an amplitude of 1.0 metre and periodic time \(\frac{11}{7}\)sec. Calculate the velocity and the kinetic energy of the particle at the moment when its displacement is 0.6 metre.

Two pendulums of lengths 100 cm and 110.25 cm start oscillating in phase simultaneously. After how many oscillations will they again be in phase together?

A block with a mass of 3.0 kg is suspended from an ideal spring having negligible mass and stretches the spring by 0.2 m.
(a) What is the force constant of the spring?
(b) What is the period of oscillation of the block if it is pulled down and released?

A SHM is expressed by the equation x = A cos (ωt + \(\phi\)) and the phase angle \(\phi\) = 0. Draw graphs to show variation of displacement, velocity and acceleration for one complete cycle in SHM.

A particle of mass 0.1 kg is held between two rigid supports by two springs of force constants 8 N/m and 2 N/m. If the particle is displaced along the direction of the length of the springs, calculate its frequency of vibration.

A simple pendulum in a stationary lift has time period T. What would be the effect on the time period when the left
(i) moves up with uniform velocity v
(ii) moves down with uniform velocity v
(iii) moves up with uniform acceleration a
(iv) moves down with uniform acceleration a
(v) beings to fall freely under gravity?

A cylindrical wooden block of cross-section 15.0 cm² and mass 230 gm is floated over water with an extra weight 50 gm attached to its bottom. The cylinder floats vertically. From the state of equilibrium, it is slightly depressed and released. If the specific gravity of wood is 0.30 and g = 9.8 m per sec², find the frequency of oscillation of the block.

What is the frequency of a second pendulum in an elevator moving up with an acceleration of \(\frac{g}{2}?\) 

The mass 'M' attached to a spring oscillates with a period 2 s. If the mass is increased by 2 kg, the period increases by 1 s. Find the initial mass 'M', assuming that Hooke's law is obeyed.