Simple Harmonic...

A particle moves along a straight line to follow the equation ax²+bv² = k, where a, b and k are constants and x and v are x-coordinate and velocity of the particle respectively. Find the amplitude.

A particle of mass m is executing oscillations about the origin on the x-axis with amplitude A. its potential energy is given as U(x) = αx⁴ where α is a positive constant. The x-coordinate of the particle where its potential energy is one third the corresponding kinetic energy is:

From the variation of potential energy in the direction of small oscillation of a simple pendulum, find the effective spring constant for the simple pendulum, where m is mass of the bob, l is length of the simple pendulum.

Initially cylindrical drums P and Q were placed at equal distance L from center of mass C of the rough rod AB in horizontal position. The drums were spinning in opposite directions with angular velocities. The rod is displaced by distance x towards left and released so that it performs SHM. If difference in reactions at Q and P is mgx/L ​where m is the mass of the rod, find the time period of oscillations, if m is the coefficient of friction:

The bob of a simple pendulum executes simple harmonic motion in water with a period t, while the period of oscillation of the bob is t₀​ in air. Neglecting frictional force of water and given that the density of the bob is (4/3) × 1000kg/m³. What relationship between t and t_0​ is true? 

A particle of mass m is attached to a spring (of spring constant k) and has a natural angular frequency ω₀. An external force F(t) proportional to cosωt (ω ≠ ω₀ ) is applied to the oscillator. The time displacement of the oscillator will be proportional to

A particle is executing SHM according to the equation x = A cos ωt. Average speed of the particle during the interval  is:

An object of mass 0.2 kg executes SHM along x-axis with a frequency of 25/π​ Hz. At the position x = 0.04 m the object  has kinetic energy 0.5 J and potential  energy 0.4 J. The amplitude of oscillation will be

A vertical mass-spring system executes simple harmonic oscillations with a period of 2s. A quantity of this system which exhibits simple harmonic variation with a period of 1 s is

A particle is performing simple harmonic motion along x-axis with amplitude 4cm and time period 1.2sec. The minimum time taken by the particle to move from x = 2cm to x = +4 cm and back. again is given by