Chapter 10 – Oscillation and Waves

Two simple harmonic motions are represented by the equations y1 = 0.1sin (100 πt + 3/π ) and y2 ​= 0.1cos πt. The phase difference of the velocity of particle 1 with respect to velocity of particle 2 is the frequency of oscillation becomes Two springs of force constants k1 and k2 are connected to [...]

The displacement of an object attached to a spring and executing simple harmonic motion is given by x = 2×10^−2 cos πt metre. The time at which the maximum speed first occurs is. The displacement of an object attached to a spring and executing simple harmonic motion is given by x = 2×10^−2 cos πt [...]

A particle of mass m executes simple harmonic motion with amplitude ‘a’ and frequency ‘v’. The average kinetic energy during its motion from the position of equilibrium to the end is : A particle of mass m executes simple harmonic motion with amplitude 'a' and frequency 'v'. The average kinetic energy during its motion from [...]

Two springs of force constants k1 and k2 are connected to a mass m as shown below. The frequency of oscillation of the mass is f. If both k1 and k2 are made four times their original values, the frequency of oscillation becomes the frequency of oscillation becomes Two springs of force constants k1 and [...]

A point mass oscillates along the x-axis according to the law x = x0 cos(ωt − 4/π ​). If the acceleration of the particle is written as a = A cos (ωt + δ), then A point mass oscillates along the x-axis according to the law x = x0 cos(ωt − 4/π ​). If the [...]

The potential energy function for the force between two atoms in a diatomic molecule is approximately given by U(x) = a/x^12 − b/x^6, where a and b are constants and x is the distance between the atoms. If the dissociation energy of the molecule is d=[U(x=∞)−U at equilibrium],then D is The potential energy function for [...]

Two particles are executing simple harmonic of the same amplitude (A) and frequency ω along the x-axis . Their mean position is separated by distance `X_(0)(X_0 > A). If the maximum separation between them is (X_(0)+A), the phase difference between their motion is:

If a spring of stiffness ‘k’ is cut into two parts ‘A’ and ‘B’ of length lA : lB = 2 : 3, then the stiffness of spring ‘A’ is given by If a spring of stiffness 'k' is cut into two parts 'A' and 'B' of length lA : lB = 2 : 3 [...]

A wooden cube (density of wood ‘d’) of side ‘l’ floats in a liquid of density ‘ρ’ with its upper and lower surfaces horizontal. If the cube is pushed slightly down and released, it performs simple harmonic motion of period ‘T’. Then, ‘T’ is equal to 'T' is equal to A wooden cube (density of [...]

If a simple pendulum has a significant amplitude (up to a factor of 1/e of original) only in the period between t=0 s to t=τ s, then τ may be called the average life of the pendulum. When the spherical Bob of the pendulum suffers a retardation (due to viscous drag) proportional to it’s velocity, [...]