Oscillations

Question

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A pan with a set of weights is attached to a light spring. The period of vertical oscillation is 0.5s. When some additional weights are put in pan, then the period of oscillations increases by 0.1 s. The extension caused by the additional weight is

5.5 cm

3.8 cm

2.7 cm

1.3 cm

Solution

2.7 cm

Given:- T = 0.5 s

We know that,

The time period for oscillation is

T = $2 π \sqrt{\frac{m}{k}}$

k = It is spring constant

m = mass

⇒ T = 0.5

⇒ 0.5 = $2 π \sqrt{\frac{m}{k}}$

⇒ $\frac{1}{4 π} = \sqrt{\frac{m}{k}}$

On squaring on both sides, we get

⇒ $\frac{m}{k} = \frac{1}{16 π^{2}}$ ....(i)

⇒ T + 0.1 = $2 π \sqrt{\frac{m + m'}{k}}$

⇒ 0.5 + 0.1 = 2 $π \sqrt{\frac{m + m'}{k}}$

⇒ ${(\frac{0.6}{2 π})}^{2} = \frac{m + m'}{k}$

⇒ = $\frac{m}{k} + \frac{m'}{k}$

⇒ $\frac{{(0.6)}^{2}}{4 π^{2}} = \frac{1}{16 π^{2}}$ + $\frac{m'}{k}$ using eq.(i)

⇒ $\frac{{(0.6)}^{2}}{4 π^{2}} - \frac{1}{16 π^{2}} = \frac{m'}{k}$

⇒ $\frac{m'}{k} = \frac{1.44 - 1}{16 π^{2}}$

⇒ $\frac{m'}{k} = \frac{0.44}{16 π^{2}}$ ....(ii)

m' g = kx

x = $\frac{m'}{k}$ g

⇒ = $\frac{0.44}{16 π^{2}}$ × 10

⇒ x = 0.0279

⇒ x = 2.79 × 10^-2 m

× x = 2.7 cm

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Oscillations

A pan with a set of weights is attached to a light spring. The period of vertical oscillation is 0.5s. When some additional weights are put in pan, then the period of oscillations increases by 0.1 s. The extension caused by the additional weight is

5.5 cm

3.8 cm

2.7 cm

1.3 cm

Some More Questions From Oscillations Chapter

A coin is placed on a horizontal platform which undergoes vertical simple harmonic motion of angular frequency ω. The amplitude of oscillation is gradually increased. The coin will leave contact with the platform for the first time

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The bob of a simple pendulum is a spherical hollow ball filled with water. A plugged hole near the bottom of the oscillation bob gets suddenly unplugged. During observation, till water is coming out, the time period of oscillation would

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For Daily Free Study Material Join wiredfaculty

Oscillations

A pan with a set of weights is attached to a light spring. The period of vertical oscillation is 0.5s. When some additional weights are put in pan, then the period of oscillations increases by 0.1 s. The extension caused by the additional weight is 5.5 cm 3.8 cm 2.7 cm 1.3 cm

Some More Questions From Oscillations Chapter

A coin is placed on a horizontal platform which undergoes vertical simple harmonic motion of angular frequency ω. The amplitude of oscillation is gradually increased. The coin will leave contact with the platform for the first time

The function sin2(ωt) represents

The bob of a simple pendulum is a spherical hollow ball filled with water. A plugged hole near the bottom of the oscillation bob gets suddenly unplugged. During observation, till water is coming out, the time period of oscillation would

The total energy of particle, executing simple harmonic motion is

In forced oscillation of a particle the amplitude is maximum for a frequency ω1 of the force, while the energy is maximum for a frequency ω2 of the force, then

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

A pan with a set of weights is attached to a light spring. The period of vertical oscillation is 0.5s. When some additional weights are put in pan, then the period of oscillations increases by 0.1 s. The extension caused by the additional weight is

5.5 cm

3.8 cm

2.7 cm

1.3 cm

The function sin²(ωt) represents

In forced oscillation of a particle the amplitude is maximum for a frequency ω₁ of the force, while the energy is maximum for a frequency ω₂ of the force, then