Physics Oscillations

Given below are two statements:

Statement I : A second's pendulum has a time period of 1 second.

Statement II : It takes precisely one second to move between the two extreme positions.

In the light of the above statements, choose the correct answer from the options given below:

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Contributor-Level 10

Kindly go through the solution

Time period of second pendulum is 2 seconds.

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A particle executes S.H.M., the graph of velocity as a function of displacement is:

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-> $v = ω \sqrt[]{A^{2} - x^{2}} \Rightarrow \frac{v^{2}}{A^{2} ω^{2}} + \frac{x^{2}}{A^{2}} = 1$ Path is ellipse.

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The potential energy (U) of a diatomic molecule is a function dependent on r (interatomic distance) as $U = \frac{α}{r^{10}} - \frac{β}{r^{5}} - 3$

Where, α and β are positive constants. The equilibrium between two atoms will be ${(\frac{2 α}{β})}^{\frac{a}{b}},$ where α =…………….

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For equilibrium,

$\frac{d U}{d r} = 0 \Rightarrow \frac{- 10 α}{r^{11}} + \frac{5 β}{r^{6}} = 0 \Rightarrow r = {(\frac{2 α}{β})}^{\frac{1}{5}}$

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A student is performing the experiment of resonance column. The diameter of the column tube is 6cm. THE Frequency of the tuning fork is 504 Hz. Speed of the sound at the given temperature is 336m/s. The zero of the meter scale coincides with tip end of the resonance column tube. The reading of the water level in the column when the first resonance occurs is:

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Physics Oscillations Oscillations

Contributor-Level 10

For first resonance,

$l + 0.3 d = \frac{v}{4 f}$

$\Rightarrow l + 0.3 * 6 = \frac{336 * 100}{4 * 504} \Rightarrow l = 14.8 c m$

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If the time period of a two meter long simple pendulum is 2s, the acceleration due to gravity at the place where pendulum is executing S.H.M. is:

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Physics Oscillations Oscillations

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$T = 2 π \sqrt[]{\frac{l}{g}}$

$\Rightarrow 2 = 2 π \sqrt[]{\frac{2}{g}}$

$\Rightarrow g = 2 π^{2} m / s^{2}$

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In the given figure, a mass M is attached to a horizontal spring which is fixed on one side to a rigid support. The spring constant of the spring is k. The mass oscillates on a frictionless surface with time period T and amplitude A. When the mass is in equilibrium position, as shown in the figure, another mass m is gently fixed upon it. New amplitude of oscillation will be:

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Velocity of block in equilibrium, in first case,

$v = A ω = A . \sqrt[]{\frac{k}{M}}$

Velocity of block in equilibrium, is second case,

$v' = A' ω' = A' \sqrt[]{\frac{k}{M + m}}$

From conservation of momentum,

Mv = (M + m) v'

$\Rightarrow M A \sqrt[]{\frac{k}{M}} = (M + m) A' \sqrt[]{\frac{k}{M + m}} \Rightarrow A' = A \sqrt[]{\frac{M}{M + m}}$

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3 months ago

The motion of a simple pendulum executing S.H.M. is represented by the following equation. $y = A s i n (π t + ?),$ where time is measured in second.

The length of pendulum is

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Contributor-Level 10

According to question, we can write

$ω = π = \sqrt[]{\frac{g}{l}} \Rightarrow l = \frac{g}{π^{2}} = \frac{9.8}{{(3.14)}^{2}} = 0.99395 = 99.4 c m$

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Time period of a simple pendulum in a stationary lift is 'T'. If the lift accelerated with $\frac{g}{6}$ vertically upwards then the time period will be:

(Where g = acceleration due to gravity)

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Raj Pandey

Contributor-Level 9

$g_{e f f} = g + a$

$= g + \frac{g}{6}$

$= \frac{7 g}{6}$

$T' = 2 π \sqrt[]{\frac{l}{g_{e f f}}}$

$T' = \sqrt[]{\frac{6}{7}} T$

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In an experiment to determine the velocity of sound in air at room temperature using a resonance tube, the first resonance is observed when the air column has a length of 20.0 cm for a tuning form of frequency 400 Hz is used. The velocity of the sound at room temperature is 336 ms^-¹. The third resonance is observed when the air column has a length of ____________cm.

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Contributor-Level 10

According to Concept of resonance tube, we can write

$\frac{λ}{4} + e = l_{1} a n d \frac{3 λ}{4} + e = l_{2} \Rightarrow \frac{λ}{2} = l_{2} - l_{1} \Rightarrow \frac{V}{2 ν} = l_{2} - l_{1}$

$\Rightarrow l_{2} = \frac{v}{2 ν} + l_{1} = \frac{336}{400} + 0.20 = 0.84 + 0.20 = 1.04 m = 104 c m$

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3 months ago

The motion of a simple pendulum executing S.H.M. is represented by the following equation. $y = A s i n (π t + ϕ),$ where time is measured in second.

The length of pendulum is

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