List of top Physics Questions on simple harmonic motion asked in MHT CET

A particle is performing S.H.M. about \(x = 0\), with an amplitude \(a\) and time period \(T\). The speed of the particle at \(x = \frac{a}{3}\) will be

The displacement of a particle varies with time according to the relation
\(x = asinωt+bcosωt\)

Two oscillating simple pendulums with time periods \(T\) and \(\frac{4T}{3}\) are in phase at a given time. They will be again in phase after an elapse of time

A spring force constant \(180\) N/m is loaded with a mass \(0.2\) kg. The amplitude of oscillations is \(4\) cm. When mass comes to equilibrium position, its velocity is

A particle executing linear S.H.M. has velocities \(V_1\) and \(V_2\) at distance \(x_1\) and \(x_2\) respectively, from the mean position, its angular velocity is

A particle executes a simple harmonic motion with a periodic time \(8\) second. At time \(t = 0\), it is at a mean position. The ratio of the distance traveled by a particle in the 2nd and that in the 1st second of its motion is
(\(sin45^{\circ} = cos45^{\circ} = \frac{1}{\sqrt{2}}\), \(sin90^{\circ} = cos0^{\circ} = 1\))

Two particles A and B of equal masses are suspended from two massless springs of spring constants \(K_A\) and \(K_B\) respectively. The maximum velocities of the particles during oscillations are equal. The ratio of the amplitude of 'B' to that of 'A' is

A particle is performing simple harmonic motion about \(x = 0\) with an amplitude '\(a\)' and periodic time T. The speed of the particle at \(x = \frac{a}{3}\) will be

The displacement of a particle performing linear S.H.M. is given by \(y = Acos[π(t+φ)]\). If at \(t = 0\), the displacement is \(y = 2\) cm and velocity is \(2π\) cm/s, the value of amplitude A in cm is

A light spring is suspended with mass '\(m_1\)' at its lower end and its upper end is fixed to a rigid support. The mass is pulled down a short distance and then released. The period of oscillation is T second. When a mass '\(m_2\)' is added to '\(m_1\)' and the system is made to oscillate the period is found to be \(\frac{3}{2}\) T. The ratio \((\frac{m_1}{m_2})\) is

A particle executing simple harmonic motion starts from mean position with amplitude '\(A\)' and periodic time '\(T\)'. At what displacement is its speed one-fourth of the maximum speed?

For a particle executing S.H.M., its potential energy is 8 times its kinetic energy at a certain displacement '\(x\)' from the mean position. If '\(A\)' is the amplitude of S.H.M., the value of '\(x\)' is

A mass \(m_1\) performs S.H.M. with amplitude A which is connected to horizontal spring. While mass \(m_1\) passing through mean position, another mass \(m_2\) (\(m_2 < m_1\)) is placed on it so that both masses move together with amplitude \(A_1\). The ratio of \(A/A_1\) is

For a particle P performing S.H.M., when displacement is 'x', potential energy and restoring force acting on it is denoted by 'E' and 'F' respectively. The relation between x, E and F is

The minimum phase difference between two simple harmonic motions is
\(x_1 = \frac{1}{\sqrt{2}}sinωt+\frac{1}{\sqrt{2}}cosωt\)
\(x_2 = sinωt+cosωt\)     \([sin\frac{π}{4} = cos\frac{π}{4} = \frac{1}{\sqrt{2}}]\)

A body of mass \(0.4\) kg performs simple harmonic motion. It experiences a restoring force of \(0.4\) N when its displacement from the mean position is 4 cm. The force constant and magnitude of acceleration respectively are

A small sphere oscillates simple harmonically in a watch glass whose radius of curvature is \(1.6\) m. The period of Oscillation of the sphere is (Acceleration due to gravity \(g = 10\text{ m/s}^2\))

A particle executes linear S.H.M. with amplitude \(4\) cm. The magnitude of velocity and acceleration is equal when it is at \(3\) cm from mean position. Time period is

The velocity of a particle executing SHM varies with displacement (\(x\)) as \(4v^2 = 50-x^2\).
The time period of oscillations is \(x/7\) s.
The value of \(x\) is (Take \(π = 22/7\))

A spring executes S.H.M. with mass 10 kg attached to it. The force constant of spring is 10 N/m. If at any instant its velocity is 40 cm/s, the displacement at that instant is
(Amplitude of S.H.M. is 0.5 m)

A mass attached to a spring performs S.H.M. whose displacement is \(x = 3\times 10^{-3}cos2πt\) m. The time taken to obtain maximum speed for the first time is (in s)

A particle executes simple harmonic motion between \(x = -A\) and \(x = +A\). If time taken by particle to go from \(x = 0\) to \(\frac{A}{2}\) is \(2\)s, then time taken by particle in going from \(x = \frac{A}{2}\) to A is

A particle performs SHM with an amplitude of 5 cm. Find its acceleration when it is 3 cm from the mean position (assume \( \omega = 2 \, \text{rad/s} \)).

A spring executes S.H.M. with mass 1 kg attached to it. The force constant of the spring is 4 N/m. If at any instant its velocity is 20 cm/s, the displacement at that instant is (Amplitude of S.H.M. is 0.4 m) ______.