The total mechanical energy of a spring-mass system in simple harmonic motion is \(E=\frac12m~\omega^2A^2\). Suppose the oscillating particle is replaced by another particle of double the mass while the amplitude A remains the same. The new mechanical energy will

1. become 2E

2. become E/2

3. become \(\sqrt E\)

4. remain E

The average energy in one time period in simple harmonic motion is:
1. \(\frac{1}{2} m \omega^{2} A^{2}\) 
2. \(\frac{1}{4} m \omega^{2} A^{2}\) 
3. \(m \omega^{2} A^{2}\)
4. zero

A particle executes simple harmonic motion with a frequency \(\nu.\) The frequency with which the kinetic energy oscillates is:
1. \(\nu/2\)
2. \(\nu\)
3. \(2\nu\)
4. zero

In a simple harmonic motion:

1. the potential energy is always equal to the kinetic energy

2. the potential energy is never equal to the kinetic energy

3. the average potential energy in any time interval is equal to the average kinetic energy in that time interval

4. the average potential energy in one time period equal to the average kinetic energy in this period

In a simple harmonic motion:

(a) the maximum potential energy equals the maximum kinetic energy

(b) the minimum potential energy equals the minimum kinetic energy

(c) the minimum potential energy equals the maximum kinetic energy

(d) the maximum potential energy equals the minimum kinetic energy

Choose the correct option:

1. (a) and (b)

2. (b) and (c)

3. (c) and (d)

4. All of these