Changing the Period of a Pendulum

Ans. The frequency of a pendulum is defined as the number of oscillations per second. It is given by

f = 1/T

Where T is the time period of the pendulum.

Given the period of the oscillation of the pendulum is, T = 4 s

On substituting the value, we get

Frequency, f = 1/T = 1/4 = 0.25 Hz

Ans. A simple pendulum consists of a heavy point mass (referred to as the bob) hanging from a rigid support by a massless and inextensible thread. A pendulum is set to motion when a bob from its mean position is pulled to one side and then released.

Ans. The time period of a simple pendulum can be calculated by the formula

T = 2π \(\sqrt{\frac{L}{g}}\)

Where L is the length of the string.

Ans. For a simple pendulum, a spherical bob is used for the following reasons:

1. The spherical shape has the smallest volume for a given density value.
2. The spherical shape reduces air friction.

Ans. Since another ball that is at rest is kept at the extreme position of the pendulum, at the extreme position, the velocity of the bob of the pendulum is zero i.e. v = 0.

Momentum at the extreme position, p = m(dv/dt) = 0

Hence momentum transferred to the ball by the bob of the pendulum is zero.

Ans. The length of the smaller pendulum, l₁ = 1 m

Therefore, its time period is, T₁ = 2π√(1/g)

The length of the bigger pendulum, l₂ = 1.21 m

Therefore, its time period is, T₂ = 2π√(1.21/g)

Taking the ratio of both time periods, we get

T₁/T₂ = [2π√(1/g)]/[2π√(1.21/g)]

⇒ T₁/T₂ = 10/11

⇒ 1₁T₁ = 10T₂

Therefore after completing 10 oscillations of the bigger pendulum, the smaller pendulum will complete 11 oscillations.

Hence after 10 oscillations of the bigger pendulum, they will again be in the same phase.

Ans. Periodic motion is a type of motion in which an object repeats its motion at regular intervals. This means that the object returns to the same position and velocity at the same time after a certain amount of time has passed.

Ans. Given

• The maximum mass that the scale can read, M = 50 kg
• The maximum displacement of the spring = Length of the scale, l = 20 cm = 0.2 m
• Time period, T = 0.6 s

Maximum force exerted on the spring, F = Mg

On substituting the values, we get

F = 50 × 9.8 = 490

Now, spring constant, k = F/l

⇒ k = 490/0.2 = 2450 N m^-1

Let mass m be suspended from the balance, then the time period of the pendulum is given by

T = 2π√(m/k)

⇒ m = (T/2π)² x k

On substituting the values, we get

m = (0.6/2x 3.14)² x 2450 = 22.36 kg

Hence, the weight of the body is, W = mg = 22.36 x 9.8 = 219 N

Ans. The restoring force of a heavy bob is sufficient to overcome air resistance. A small bob has less resistance due to air. As a result, a heavy bob having a small size is used as a bob in a simple pendulum.

Ans. The time period and frequency are inversely proportional to each other, and it is given by

f = 1/T

Where f is the frequency and T is the time period.

Ans. The frequency of a pendulum is defined as the number of oscillations per second. It is given by

f = 1/T

Where T is the time period of the pendulum.

Given the period of the oscillation of the pendulum is, T = 2 s

On substituting the value, we get

Frequency, f = 1/T = 1/2 = 0.5 Hz

Ans. Simple harmonic motion (SHM) is a special type of periodic motion in which the restoring force is directly proportional to the displacement of the object from its equilibrium position and acts towards the equilibrium position.

Ans. The time period of a simple pendulum is given by

T = 2π√(l/g)

From the above equation, for the constant value of g, the time period of the simple pendulum is directly proportional to the square root of its length i.e.

T ∝ √l

⇒ T₁/T₂ = (√l₁)/(√l₂)

Where 

• T₁ and T₂ are the initial and final time periods.
• l₁ and l₂ are the initial and final lengths of the string of the pendulum.

Given

• T₁ = √2 s
• l₂ = l₁/2

On substituting the values, we get

(√2)/T₂ = (√l₁)/(√l₁/2) = √2

⇒ T₂ = 1s

Hence, the new time period will be 1 second.

Ans. The time period of a pendulum is the time it takes to complete one full oscillation. It is the time it takes for the pendulum to swing from one side to the other and back again. The time period is denoted by the letter T and is measured in seconds (s).

Ans. Oscillatory motion is a type of motion in which an object moves back and forth repeatedly about a fixed point. This fixed point is called the equilibrium position. Oscillatory motion is a special type of periodic motion, which means that the object repeats its motion at regular intervals.