Asimple pendulum 2 m long swings through a maximum angle of 30 ∘ with the vertical. part a calculate its period assuming a small amplitude.

Length of the pendulum (l) = 2 m

Acceleration due to gravity = g = 9.8 m/s^2

For small amplitude, the pendulum will undergo simple harmonic motion.

Hence, the time period of the pendulum for small amplitude =

Now, plug the values of l and g

T =

T = 2 × 3.14 × 0.451

T = 2.83 seconds

Hence, the time period of the pendulum for small amplitude = 2.83 s

The time period of the pendulum performing the oscillation of small amplitude is .

Further Explanation:

Given:

The length of the simple pendulum is .

The maximum angle of the pendulum’s oscillation is .

Concept:

If the amplitude of oscillation of the simple pendulum is very small, then the oscillation of the pendulum is termed as the simple harmonic.

The time period of a given pendulum is independent of the mass of the bob and amplitude of oscillation. It depends on the length and the acceleration due to gravity of the Earth.

The time period of a pendulum exhibiting simple harmonic motion is given as:

                        …… (1)

Here, is the time period of oscillation of the pendulum, is the length of the pendulum and is the acceleration due to gravity of the Earth.

The value of acceleration due to gravity on the Earth is .

Substitute the values of length and acceleration due to gravity in above expression.

Thus, the time period of the pendulum performing the oscillation of small amplitude is .

Learn More:

1. The amount of kinetic energy an object has depends on its

2. A 700-kg car, driving at 29 m/s, hits a brick wall and rebounds with a speed of 4.5 m/s

3. If forces acting on an object are unbalanced, the object could experience a change in , direction, or both

Answer Details:

Grade: Middle School

Subject: Physics

Chapter: Simple Harmonic Motion

Keywords:

Simple pendulum, harmonic motion, maximum angle, 30 degree, with vertical, oscillation, time period, small amplitude.

scattering of light by tiny particles in air to produce the colors we see on sky, is dependent on the following factors:

(i) wavelength of light

(ii) size of the scattering particle  

(iii) distance traveled by light through the atmosphere.

according to rayleigh's law of scattering, the amount of scattering is inversely proportional to the fourth power of its wavelength. shorter the wavelength, greater is its scattering. hence violet/blue light is scattered more than red.

sun's light is a composite light ( visible light) with wavelengths in the range 400 nm (violet) to 700 nm (red). as sunlight passes through our atmosphere, the molecules of air scatter light according to their wavelengths. during sunrise and sunset, the sun's position is below the horizon. hence light from the sun travels a greater distance in the atmosphere when compared to its position a noon.

as sunlight enters the earth's atmosphere, blue light is scattered away and at the end of its journey in the sky, only red and orange wavelengths remain in the beam.

hence at sunrise and sunset, the sky appears reddish orange.