Method to determine Time Period and Frequency PYQs: JEE Mains Physics

Showing 1–19 of 19 questions

1. 1. A cylindrical block of mass M and area of cross section A is floating in a liquid of density \(\rho\) and with its axis vertical. When depressed a little and released the block starts oscillating. The period of oscillation is _________ . 2026 Medium
2. 2. A light hollow cube of side length 10 cm and mass 10 g , is floating in water. It is pushed down and released to execute simple harmonic oscillations. The time period of oscillations is \(y \pi \times 10^{-2} \mathrm{~s}\), where the value of \(y\) is ________.
   (Acceleration due to gravity, \(g=10 \mathrm{~m} / \mathrm{s}^2\), density of water \(=10^3 \mathrm{~kg} / \mathrm{m}^3\) ) 2025 Hard
3. 3. A particle of mass \(0.50 \mathrm{~kg}\) executes simple harmonic motion under force \(\mathrm{F}=-50\left(\mathrm{Nm}^{-1}\right) \mathrm{x}\). The time period of oscillation is \(\frac{x}{35} s\). The value of \(x\) is _______. (Given \(\pi=\frac{22}{7}\) ) 2024 Hard
4. 4. To find the spring constant \((k)\) of a spring experimentally, a student commits \(2 \%\) positive error in the measurement of time and \(1 \%\) negative error in measurement of mass. The percentage error in determining value of \(\mathrm{k}\) is _______. 2024 Hard
5. 5. A mass \(m\) attached to free end of a spring executes SHM with a period of \(1\; s\). If the mass is increased by \(3\; kg\) the period of oscillation increases by one second, the value of mass \(m\) is \(..............kg\). 2023 Medium
6. 6. Assume that the earth is a solid sphere of uniform density and a tunnel is dug along its diameter throughout the earth. It is found that when a particle is released in this tunnel, it executes a simple harmonic motion. The mass of the particle is \(100 g\). The time period of the motion of the particle will be (approximately) (take \(g =10\,ms ^{-2}\), radius of earth \(=6400\,km\) ) 2023 Medium
7. 7. For a simple harmonic motion in a mass spring system shown, the surface is frictionless. When the mass of the block is \(1\,kg\), the angular frequency is \(\omega_1\). When the mass block is \(2\,kg\) the angular frequency is \(\omega_2\). The ratio \(\omega_2 / \omega_1\) is
   2023 Easy
8. 8. Assume that a tunnel is dug along a chord of the earth, at a perpendicular distance \(( R / 2)\) from the earth's centre, where \('R'\) is the radius of the Earth. The wall of the tunnel is frictionless. If a particle is released in this tunnel, it will execute a simple harmonic motion with a time period 2021 Hard
9. 9. The function of time representing a simple harmonic motion with a period of \(\frac{\pi}{\omega}\) is : 2021 Hard
10. 10. A ring is hung on a nail. It can oscillate, without slipping or sliding \((i)\) in its plane with a time period \(T_{1}\) and, \((ii)\) back and forth in a direction perpendicular to its plane, with a period \(T _{2}\). the ratio \(\frac{ T _{1}}{ T _{2}}\) will be  2020 Hard
11. 11. An object of mass \(m\) is suspended at the end of a massless wire of length \(L\) and area of cross\(-\)section, \(A\). Young modulus of the material of the wire is \(Y\). If the mass is pulled down slightly its frequency of oscillation along the vertical direction is 2020 Medium
12. 12. A person of mass \(M\) is, sitting on a swing of length \(L\) and swinging with an angular amplitude \(\theta_0\). If the person stands up when the swing passes through its lowest point, the work done by him, assuming that his centre of mass moves by a distance \(l\, ( l < < L)\), is close to 2019 Hard
13. 13. A rod of mass \(‘M’\) and length \(‘2L’\) is suspended at its middle by a wire. It exhibits torsional oscillations; If two masses each of \(‘m’\) are attached at distance \(‘L/2’\) from its centre on both sides, it reduces the oscillation frequency by \(20\%\). The value of ratio \(m/M\) is close to 2019 Hard
14. 14. A simple pendulum oscillating in air has period \(T.\) The bob of the pendulum is completely immersed in a non-viscous liquid. The density of the liquid is \(\frac {1}{16}\) of the material of the bob. If the bob is inside liquid all the time, its period of oscillation in this liquid is 2019 Hard
15. 15. Two light identical springs of spring constant \(k\) are attached horizontally at the two ends of a uniform horizontal rod \(AB\) of length \(l\) and mass \(m\). the rod is pivoted at its centre \(‘O’\) and can rotate freely in horizontal plane. The other ends of the two springs are fixed to rigid supports as shown in figure. The rod is gently pushed through a small angle and released. The frequency of resulting oscillation is
    2019 Hard
16. 16. silver atom in a solid oscillates in simple harmonic motion in some direction with a frequency of \(10^{12}  /sec\). What is the force constant of the bonds connecting one atom with the other? ................ \(\mathrm{N/m}\)     (Mole wt. of silver \(= 108 \) andAvagadro number \(= 6.02 \times 10^{23}\) \(gm \ mole^{ -1}\) ) 2018 Medium
17. 17. pendulum made of a uniform wire of cross sectional area \(A\) has time period \(T\). When an additional mass \(M\) is added to its bob, the time period changes to \(T_M\). If the Young's modulus of the material of the wire is \(Y\) then \(\frac{1}{Y}\) is equal to : (\(g\) = gravitational acceleration) 2015 Hard
18. 18. particle moves with simple harmonic motion in a straight line. In first \(\tau\ s\), after starting from rest it travels a distance \(a\), and in next \(\tau\ s\) it travels \(2a\), in same direction, then 2014 Hard
19. 19. An ideal gas enclosed in a vertical cylindrical container supports a freely moving piston of mass \(M\). The piston and the cylinder have equal cross sectional area \(A\). When the piston is in equilibrium, the volume of the gas is \(V_0\) and its pressure is \(P_ 0\). The piston is slightly displaced from the equilibrium position and released. Assuming that the system is completely isolated from its surrounding, the piston executes a simple harmonic motion with frequency 2013 Hard

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