Mechanics SHM Mock Tests

A simple pendulum of length L and mass m has a period T_0 in a stationary frame. The pendulum is now placed in an elevator accelerating upward with acceleration a = g/3. The new period T is:

A particle of mass m moves in one dimension under the potential V(x) = alpha x^4 - beta x^2 where alpha > 0 and beta > 0. For small oscillations about the stable equilibrium position, the frequency of oscillation is:

A simple pendulum of length L has a period T on Earth. If the pendulum is taken to a height h above the Earth surface where the gravitational acceleration becomes (2/3)g, its new period is:

A particle undergoes two perpendicular SHMs: x(t) = A cos(ωt) and y(t) = B cos(ωt + φ) where A ≠ B and φ = π/2. The trajectory of the particle is:

A simple pendulum of length L has period T on Earth. If the same pendulum is taken to a planet where the gravitational acceleration is g/4, the new period is:

A uniform solid cylinder of mass M and radius R is placed inside a fixed hollow cylinder of radius 2R. The smaller cylinder rolls without slipping inside the larger one. For small oscillations, the angular frequency of oscillation is:

A particle executes simple harmonic motion described by x(t) = A cos(omega t + phi). At t = 0, the particle is at x = A/sqrt(2) moving in the positive x direction. The phase constant phi is:

A mass m is attached to a spring of spring constant k and oscillates with amplitude A on a frictionless surface. The mass is replaced by a mass 4m and the spring is changed to one with spring constant 4k, keeping the total energy the same. The new amplitude is: