Oscillation and Simple Harmonic Motion | Physics JEE previous year questions with Solutions

Q 1 :
A simple pendulum doing small oscillations at a place R height above earth surface has time period of $T_{1} = 4 s .$ $T_{2}$ would be it's time period if it is brought to a point which is at a height 2R from earth surface.

Choose the correct relation [R = radius of earth] [2024]

$2 T_{1} = 3 T_{2}$
$2 T_{1} = T_{2}$
$T_{1} = T_{2}$
$3 T_{1} = 2 T_{2}$

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(D) $T = 2 π \sqrt{\frac{l}{g}} = 2 π \sqrt{\frac{l r^{2}}{GM}} = 2 π \sqrt{\frac{l}{GM}} r$

$\Rightarrow \frac{T_{2}}{T_{1}} = \frac{r_{2}}{r_{1}} = \frac{3 R}{2 R} \Rightarrow 2 T_{2} = 3 T_{1}$

Q 2 :
A mass m is suspended from a spring of negligible mass and the system oscillates with a frequency $f_{1}$ . The frequency of oscillations if a mass 9 m is suspended from the same spring is $f_{2} .$ The value of $\frac{f_{1}}{f_{2}}$ is _______ . [2024]

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(3)

Q 3 :
In simple harmonic motion, the total mechanical energy of a given system is E. If the mass of oscillating particle P is doubled, then the new energy of the system for same amplitude is [2024]

[IMAGE 121]

$E \sqrt{2}$
$E$
$2 E$
$E / \sqrt{2}$

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(2)

Total energy $E = K E + P E$

$E = \frac{1}{2} m ω^{2} (A^{2} - x^{2}) + \frac{1}{2} m ω^{2} x^{2}$

$E = \frac{1}{2} k A^{2}, since A is same, T . E . will be same$

Q 4 :
The time period of simple harmonic motion of mass M in the given figure is $π \sqrt{\frac{α M}{5 k}},$ where the value of $α$ is ________ . [2024]

[IMAGE 122]

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(12)

$k_{eq} = \frac{2 k \cdot k}{3 k} + k = \frac{5 k}{3}$

Angular frequency of oscillation $(ω) = \sqrt{\frac{k_{eq}}{m}}$

$(ω) = \sqrt{\frac{5 k}{3 m}}$

Period of oscillation $(τ) = \frac{2 π}{ω} = 2 π \sqrt{\frac{3 m}{5 k}}$

$= π \sqrt{\frac{12 m}{5 k}}$

Topic Question Set

Q 1 :
A simple pendulum doing small oscillations at a place R height above earth surface has time period of $T_{1} = 4 s .$ $T_{2}$ would be it's time period if it is brought to a point which is at a height 2R from earth surface.

Choose the correct relation [R = radius of earth] [2024]

Q 2 :
A mass m is suspended from a spring of negligible mass and the system oscillates with a frequency $f_{1}$ . The frequency of oscillations if a mass 9 m is suspended from the same spring is $f_{2} .$ The value of $\frac{f_{1}}{f_{2}}$ is _______ . [2024]

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Q 3 :
In simple harmonic motion, the total mechanical energy of a given system is E. If the mass of oscillating particle P is doubled, then the new energy of the system for same amplitude is [2024]

[IMAGE 121]

Q 4 :
The time period of simple harmonic motion of mass M in the given figure is $π \sqrt{\frac{α M}{5 k}},$ where the value of $α$ is ________ . [2024]

[IMAGE 122]

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Topic Question Set

Q 1 : A simple pendulum doing small oscillations at a place R height above earth surface has time period of T1=4s. T2 would be it's time period if it is brought to a point which is at a height 2R from earth surface. Choose the correct relation [R = radius of earth] [2024]

Q 2 : A mass m is suspended from a spring of negligible mass and the system oscillates with a frequency f1. The frequency of oscillations if a mass 9 m is suspended from the same spring is f2. The value of f1f2 is _______ . [2024]

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Q 3 : In simple harmonic motion, the total mechanical energy of a given system is E. If the mass of oscillating particle P is doubled, then the new energy of the system for same amplitude is [2024] [IMAGE 121]

Q 4 : The time period of simple harmonic motion of mass M in the given figure is παM5k, where the value of α is ________ . [2024] [IMAGE 122]

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Q 1 :
A simple pendulum doing small oscillations at a place R height above earth surface has time period of $T_{1} = 4 s .$ $T_{2}$ would be it's time period if it is brought to a point which is at a height 2R from earth surface.

Choose the correct relation [R = radius of earth] [2024]

Q 2 :
A mass m is suspended from a spring of negligible mass and the system oscillates with a frequency $f_{1}$ . The frequency of oscillations if a mass 9 m is suspended from the same spring is $f_{2} .$ The value of $\frac{f_{1}}{f_{2}}$ is _______ . [2024]

Q 3 :
In simple harmonic motion, the total mechanical energy of a given system is E. If the mass of oscillating particle P is doubled, then the new energy of the system for same amplitude is [2024]

[IMAGE 121]

Q 4 :
The time period of simple harmonic motion of mass M in the given figure is $π \sqrt{\frac{α M}{5 k}},$ where the value of $α$ is ________ . [2024]

[IMAGE 122]