Download App

Oscillations — Physics STD 11 Science — Question

Rajasthan BoardEnglish MediumSTD 11 SciencePhysicsOscillations3 Marks
Question
Answer the following questions:

The motion of a simple pendulum is approximately simple harmonic for small angle oscillations. For larger angles of oscillation, a more involved analysis shows that T is greater than $2\pi\sqrt{\frac{\text{l}}{\text{g}}}.$ Think of a qualitative argument to appreciate this result.

✓

Answer

In the case of a simple pendulum, the restoring force acting on the bob of the pendulum is given as:
$\text{F}=-\text{mg}\sin\theta$
Where,
F = Restoring force
m = Mass of the bob
g = Acceleration due to gravity
$\theta=$ Angle of displacement
For small $\theta,\ \sin\theta\simeq\theta$
For large $\theta,\ \sin\theta$ is greater than $\theta.$
This decreases the effective value of g.
Hence, the time period increases as:
$\text{T}=2\pi\sqrt{\frac{\text{l}}{\text{g}}}$
Where, l is the length of the simple pendulum.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "3 Marks Question" from Oscillations→Oscillations — all question types→Physics STD 11 Science question papers→Rajasthan Board STD 11 Science question papers→Rajasthan Board question paper generator→

Similar questions

In an elastic collision of two billiard balls, which of the following quantities remain conserved during the short time of collision of the balls (i.e., when they are in contact).
  1. Kinetic energy.
  2. Total linear momentum?
Give reason for your answer in each case.
→
A body of mass 60kg is dragged with just enough force to start moving on a rough surface with coefficients of static and kinetic friction 0.5 and 0.4 respectively on applying the same force. What is the acceleration?
→
A copper plate has an area of 250cm2 at 0°C. Calculate the area of this plate at 60°C. Given coefficient of linear expansion of copper is 1.7 × 10-5°C-1.
→
Calculate the change in internal energy of a gas kept in a rigid container when 100J of heat is supplied to it.
→
A horizontal platform with an object placed on it is executing SHM in the vertical direction. The amplitude of oscillation is 2.5cm. What must be the least period of these oscillations so that the object is not detached from the platform? Take g = 10ms-2?
→
Figure shows a smooth track, a part of which is a circle of radius R. A block of mass m is pushed against a spring of spring constant k fixed at the left end and is then released. Find the initial compression of the spring so that the block presses the track with a force mg when it reaches the point P, where the radius of the track is horizontal.
→
Define 'Radius of Gyration'. Derive an expression for it.
→
In a sonometer cord of length 24.7cm, resonance occurs with a tuning fork of frequency 256Hz. Deduce the velocity of the waves over the cord. At what length will resonance be observed with tuning fork of frequency 453Hz?
→
One mole of an ideal gas is taken in a Carnot engine working between 27°C and 227°C. The useful work done in one cycle is 600J. Calculate the ratio of the volume of the gas at the end and beginning of the isothermal expansion. Given R = 8.31J mole-1 K-1.
→
A U-tube contains water and methylated spirit separated by mercury. The mercury columns in the two arms are in level with 10.0cm of water in one arm and 12.5cm of spirit in the other. What is the specific gravity of spirit?
→