Simple harmonic motion and its equation, phase, oscillations of a spring, restoring force and force constant - One Line Questions
1.
What is the total energy of a simple harmonic oscillator with mass m, angular frequency ω, and amplitude A? —
Both A and B
2.
What is the phase of an oscillator when it is at its maximum positive displacement? —
π
3.
What is the phase of an oscillator when it is at its equilibrium position and moving in the positive direction? —
π/2
4.
What is the phase of an oscillator at t=0 if its equation is x(t) = 5 cos(2t + π/4) cm? —
π/4
5.
If the displacement of an object in SHM is given by x(t) = A sin(ωt), its velocity at time t = T/4 (where T is the time period) will be: —
Aω
6.
What is the phase difference between displacement and velocity in SHM? —
π/2 radians (90 degrees)
7.
What is the phase difference between displacement and acceleration in SHM? —
π radians (180 degrees)
8.
A mass of 2 kg is attached to a spring with a force constant of 8 N/m. What is the angular frequency of oscillation? —
2 rad/s
9.
If a spring has a force constant of 200 N/m, how much force is required to stretch it by 0.1 m? —
20 N
10.
The time period of a mass-spring system is 2 seconds. If the mass is doubled, what will be the new time period? —
2√2 seconds
11.
A mass of 0.5 kg oscillates on a spring with a force constant of 50 N/m. What is the frequency of oscillation? —
10/(2π) Hz
12.
What is the equation for the acceleration of a particle in SHM, given its displacement x(t) = A sin(ωt + φ)? —
a(t) = -Aω² sin(ωt + φ)
13.
In the equation of SHM, x(t) = A sin(ωt + φ), what does 'A' represent? —
Amplitude
14.
At what position in SHM is the velocity maximum? —
At the equilibrium position (x=0).
15.
At what position in SHM is the acceleration maximum? —
At the extreme positions (x = ±A).
16.
A particle performs SHM. When is its speed zero? —
At the extreme ends of its motion.
17.
A particle performs SHM. When is its speed maximum? —
At the equilibrium position.
18.
Hooke's Law for a spring states that the restoring force (F) is: —
Directly proportional to the displacement (x) and acts in the opposite direction.
19.
In the equation F = -kx, what does 'k' represent? —
Force constant
20.
In SHM, the acceleration is proportional to: —
Displacement and in the opposite direction.
21.
Consider a mass m attached to a spring with force constant k. If the mass is displaced by x from equilibrium and released, the restoring force is given by: —
F = -kx
22.
The frequency (f) of oscillation for a mass-spring system is related to the time period (T) by: —
f = 1/T
23.
What is the unit of angular frequency (ω) in SHM? —
24.
The restoring force in SHM is given by F = -kx. The negative sign indicates that the force: —
Acts opposite to the direction of displacement.
25.
What is the effect of damping on an oscillator? —
It decreases the amplitude and may slightly decrease the frequency.
26.
If the amplitude of SHM is doubled, what happens to the total energy of the oscillator? —
It quadruples.
27.
Consider a spring with force constant k. If it is cut into 'n' equal parts, the force constant of each part will be: —
nk
28.
When a particle undergoes SHM, its velocity is maximum when its displacement is: —
Minimum (zero)
29.
For a mass-spring system, if the mass is quadrupled, the time period of oscillation will: —
Double.
30.
For a mass-spring system, if the force constant is quadrupled, the time period of oscillation will: —
Halve.
31.
What is the relationship between the time period (T) and angular frequency (ω) in SHM? —
T = 2π/ω
32.
What is the defining characteristic of Simple Harmonic Motion (SHM)? —
The restoring force is directly proportional to the displacement from equilibrium and acts in the opposite direction.
33.
The potential energy is maximum in SHM at: —
The extreme positions.
34.
The kinetic energy is maximum in SHM at: —
The equilibrium position.
35.
For a simple harmonic oscillator, the potential energy is zero at: —
The equilibrium position.
36.
For a mass attached to a spring, what is the restoring force? —
The force that tends to bring the mass back to its equilibrium position.
37.
If the force constant (k) of a spring increases, what happens to the frequency (f) of oscillation, assuming the mass (m) remains the same? —
The frequency increases.
38.
The phase constant (φ) in the equation of SHM determines: —
The initial position of the oscillator at t=0.
39.
A system is undergoing SHM. Its acceleration is given by a = -ω²x. This equation implies: —
The restoring force is proportional to displacement and directed towards the mean position.
40.
What does a larger force constant (k) for a spring indicate? —
The spring is stiffer and requires more force to stretch or compress.
41.
If the mass (m) attached to a spring increases, what happens to the time period (T) of oscillation, assuming the force constant (k) remains the same? —
The time period increases.
42.
If a system exhibits SHM, its total mechanical energy is conserved if: —
No external non-conservative forces act on the system.
43.
The equation of motion for a particle is d²x/dt² = -ω²x. This describes: —
Simple Harmonic Motion.
44.
What is the equation for the velocity of a particle in SHM, given its displacement x(t) = A sin(ωt + φ)? —
v(t) = Aω cos(ωt + φ)
45.
Which quantity remains constant in a freely oscillating mass-spring system (neglecting damping)? —
Total mechanical energy
46.
In the equation x(t) = A cos(ωt + φ), if φ = 0, what is the initial position (at t=0)? —
x = A
47.
In the equation x(t) = A sin(ωt + φ), if φ = π/2, what is the initial position (at t=0)? —
x = A
48.
Which of the following equations represents Simple Harmonic Motion? —
Both A and B
49.
What is the minimum value of the force constant 'k' for a spring that can undergo SHM without deformation? —
There is no theoretical minimum other than positive
50.
The angular frequency (ω) of a mass-spring system is given by which formula? —
ω = sqrt(k/m)