The time period of a particle in simple harmonic motion is equal to the time between consecutive appearances of the particle at a particular point in its motion. This point is:
1. | the mean position |
2. | an extreme position |
3. | between the mean position and the positive extreme |
4. | between the mean position and the negative extreme |
The average energy in one time period in simple harmonic motion is:
1. \(\dfrac{1}{2} m \omega^{2} A^{2}\)
2. \(\dfrac{1}{4} m \omega^{2} A^{2}\)
3. \(m \omega^{2} A^{2}\)
4. zero
A spring-mass system oscillates with a frequency \(\nu.\) If it is taken in an elevator slowly accelerating upward, the frequency will:
1. increase
2. decrease
3. remain same
4. become zero
A particle moves in a circular path with a continuously increasing speed. Its motion is:
1. periodic
2. oscillatory
3. simple harmonic
4. none of them
Trains travel between station A and station B: on the way up (from A to B) - they travel at a speed of \(80\) km/h, while on the return trip the trains travel at twice that speed. The services are maintained round the clock. Trains leave station A every \(30\) min for station B and reach B in \(2\) hrs. All trains operate continuously, without any rest at A or B.
1. | the frequency of trains leaving B must be twice as much as A. |
2. | the frequency of trains leaving B must be half as much as A. |
3. | the frequency of trains leaving B is equal to that at A |
4. | the situation is impossible to maintain unless larger number of trains are provided at A. |
The maximum speed and acceleration of a particle undergoing SHM are \(v_0\) and \(a_0,\) respectively. The time period of the SHM is:
1. \(\frac{2\pi v_0}{a_0}\)
2. \(\frac{2\pi a_0}{v_0}\)
3. \(\frac{v_0}{a_0}\)
4. \(\frac{2v_0}{a_0}\)
A particle moves in the x-y plane according to the equation
\(x = A \cos^2 \omega t\) and \(y = A \sin^2 \omega t\)
Then, the particle undergoes:
1. | \(x + y = A\) | uniform motion along the line
2. | \(x^2 + y^2 = A^2\) | uniform circular motion along
3. | \(x + y = A\) | SHM along the line
4. | \(x^2 + y^2 = A^2\) | SHM along the circle
1. | uniform circular motion |
2. | elliptical motion |
3. | linear SHM |
4. | angular SHM along a circle |
1. | \(8\) | 2. | \(11\) |
3. | \(9\) | 4. | \(10\) |
During simple harmonic motion of a body, the energy at the extreme position is:
1. | both kinetic and potential |
2. | is always zero |
3. | purely kinetic |
4. | purely potential |