Which of the following examples represent periodic motion?

The figure depicts four \((\mathrm{x\text-t})\) plots for the linear motion of a particle.

(a)
(b)
(c)
(d)

Which of the following is true​​​​​?
1. (a) is periodic but (c) is not periodic.
2. (b) is periodic but (d) is not periodic.
3. (b) and (d) are periodic.
4. only (c) is periodic.

A particle is in linear simple harmonic motion between two points, \(A\) and \(B\), \(10~\text{cm}\) apart. (Take the direction from \(A\) to \(B\) as the positive direction.) The signs of velocity, acceleration, and force on the particle when it is at \(3~\text{cm}\) away from \(A\) going towards \(B\) are:

Which of the following relationships between the acceleration \(a\) and the displacement \(x\) of a particle involves simple harmonic motion?
1. \(a =   0 . 7 x\)
2. \(a =   - 200 x^{2} \)
3. \(a =   - 10 x\)
4. \(a =   100   x^{3}\)

A spring balance has a scale that reads from 0 to 50 kg. The length of the scale is 20 cm. A body suspended from this balance, when displaced and released, oscillates with a period of 0.6 s. What is the weight of the body?

1. 219 N

2. 196 N

3. 223 N

4. 225 N

A spring having a spring constant of \(1200\) N/m is mounted on a horizontal table as shown in the figure. A mass of \(3\) kg is attached to the free end of the spring. The mass is then pulled sideways to a distance of \(2.0\) cm and released. The frequency of oscillations will be:
    

A spring having a spring constant of \(1200\) N/m is mounted on a horizontal table as shown in the figure. A mass of \(3\) kg is attached to the free end of the spring. The mass is then pulled sideways to a distance of \(2.0\) cm and released. The maximum acceleration of the mass is: