1. Which of the following quantities remains constant during simple harmonic motion (SHM)?
Answer:
Explanation:
In SHM, although kinetic and potential energies change, their sum, which is the total mechanical energy, remains constant.
2. In a simple pendulum, at what position is the potential energy maximum?
Answer:
Explanation:
At the extreme position, the pendulum has reached its maximum displacement, and thus, its potential energy is at a maximum.
3. If the amplitude of a simple harmonic oscillator is doubled, its period will:
Answer:
Explanation:
The period of SHM does not depend on amplitude.
4. What kind of force acts on a body performing SHM?
Answer:
Explanation:
A restoring force proportional to its displacement and acting in the opposite direction is always acting on a body in SHM.
5. The time period of a simple pendulum of length L on the surface of Earth is T. What will be its time period on a planet where acceleration due to gravity is half of that on Earth?
Answer:
Explanation:
Time period T is directly proportional to 1/√g. If g is halved, T will become √2 times.
6. For a spring-block oscillator, the time period T is given by:
Answer:
Explanation:
The time period for a spring-block system is given by T = 2π√(m/k), where m is the mass and k is the spring constant.
7. Which of the following is a necessary condition for SHM?
Answer:
Explanation:
For SHM, the restoring force is zero at the mean position.
8. The displacement of a body performing SHM is given by x = A sin(ωt + φ). Here, φ represents:
Answer:
Explanation:
In the equation, φ represents the initial phase or phase constant.
9. The maximum velocity of a body in SHM is given by:
Answer:
Explanation:
The maximum velocity Vmax = ωA, where ω is the angular frequency and A is the amplitude.
10. In SHM, acceleration is directly proportional to:
Answer:
Explanation:
Acceleration in SHM is directly proportional to the displacement and is directed towards the mean position.
11. The potential energy of a harmonic oscillator is zero at:
Answer:
Explanation:
At the mean position, the displacement is zero; hence, potential energy is zero.
12. If the frequency of a harmonic oscillator is 10 Hz, its time period will be:
Answer:
Explanation:
Time period T = 1/frequency. Therefore, T = 1/10 = 0.1 s.
13. A body is in SHM. When its displacement is half of the amplitude, what fraction of its total energy is kinetic?
Answer:
Explanation:
When displacement is half of the amplitude, the kinetic energy is 3/4th of the total energy.
14. The angular frequency (ω) of a body in SHM is related to the time period (T) as:
Answer:
Explanation:
Angular frequency ω = 2π times the frequency, and frequency = 1/T. Thus, ω = 2π/T.
15. A body is oscillating with a time period of 2 seconds. Its frequency is:
Answer:
Explanation:
Frequency = 1/Time period. Therefore, frequency = 1/2 = 0.5 Hz.