Oscillations and Spring Dynamics

The video tutorial explains the time period of a loaded spring. It begins by describing a spring suspended vertically with a mass, detailing its equilibrium position. The spring's oscillations and displacement are discussed, followed by the restoring force and Newton's second law. The motion is compared to simple harmonic motion, leading to the derivation of the time period formula, which shows it is proportional to the square root of the mass and inversely proportional to the square root of the spring's force constant.

What happens to a spring when it is pulled down slightly and released?

• It breaks due to tension.

• It oscillates vertically about the mean position.

• It moves horizontally.

• It remains in the new position.

What is the role of the force constant 'K' in the context of a spring?

• It defines the stiffness of the spring.

• It is unrelated to the spring's behavior.

• It determines the mass of the spring.

• It measures the length of the spring.

According to Newton's second law, what is the relationship between force and acceleration in the context of a spring?

• Force is inversely proportional to acceleration.

• Force is equal to the square of acceleration.

• Force is directly proportional to acceleration.

• Force is unrelated to acceleration.

How is acceleration related to displacement in the oscillation of a spring?

• Acceleration is directly proportional to displacement.

• Acceleration is inversely proportional to displacement.

• Acceleration is directly proportional to the negative of displacement.

• Acceleration is unrelated to displacement.

What is the angular frequency 'Omega' in terms of the force constant 'K' and mass 'M'?

• Omega is equal to the square root of K divided by M.

• Omega is equal to the square root of M divided by K.

• Omega is equal to K divided by M.

• Omega is equal to M divided by K.

In the context of a loaded spring, what does the term 'simple harmonic motion' imply?

• The motion is chaotic and irregular.

• The motion is periodic and follows a sinusoidal pattern.

• The motion is linear and non-repetitive.

• The motion is random and unpredictable.

What is the formula for the time period 'T' of a loaded spring?

• T = 2π * square root of K by M

• T = 2π * M

• T = 2π * square root of M by K

• T = 2π * K

How does the time period of a loaded spring change with an increase in mass?

• The time period decreases.

• The time period increases.

• The time period becomes zero.

• The time period remains constant.

What is the effect of increasing the force constant 'K' on the time period of a spring?

• The time period becomes infinite.

• The time period remains unchanged.

• The time period decreases.

• The time period increases.