Which one of the following is simple harmonic ?

• Rotation of earth around the sun

• Rotation of earth about its own axis

• Motion of oscillating liquid column in U-tube

• Motion of a steel ball in a viscous medium

A magnet takes a minute to make 30 oscillations in a magnetic field. If the field strength is doubled, then the time period of oscillation (in sec) is

• $\sqrt{2}$

• $2\sqrt{2}$

• $\frac{\sqrt{3}}{2}$

• $\sqrt{3}$

If the time period of oscillation of a pendulum is measured as 2.5 s using a stop watch with the leas tcount $\frac{1}{2}$s, then the permissible error in the measurement is

• 10 %

• 30 %

• 20 %

• 25 %

A body of mass 4.9 kg hangs from a spring and oscillates with a period 0.5 s. On the removal of the body, the spring is shortened by (Take g = 10 ms^-2, ${\mathrm{\pi }}^2$ = 10)

• 6.3 m

• 0.63 m

• 6.25 cm

• 63 cm

The amplitude of a damped oscillator becomes $\left(\frac{1}{3}\right)$rd in 2s. If its amplitude after 6 s is $\frac{1}{\mathrm{n}}$ times the original amplitude, the value of n is

• 3²

• $\sqrt[3]{2}$

• 3³

• 2³

56.

If two springs A and B with spring constants 2 k and k, are stretched separately by same suspended weight, then the ratio between the work done in stretching A and B is

• 1 : 2

• 1 : 4

• 1 : 3

• 4 : 1

A particle oscillating under a force $\overrightarrow{\mathrm{F}} - -\mathrm{k}\overrightarrow{\mathrm{x}} - \mathrm{b}\overrightarrow{\mathrm{v}}$ is a (k and b are constants)

• simple harmonic oscillator

• non linear oscillator

• damped oscillator

• forced oscillator

A mass of 4 kg suspended from a spring of force constant 800 Nm^-1 executes simple harmonic oscillations. If the total energy of the oscillator is 4 J, the maximum accelerations (in ms^-2) of the mass is

• 5

• 15

• 45

• 20

An electric motor of mass 40 kg is mounted on four vertical springs each having a spring constant of 4000 Nm^-1. The period with which the motor vibrates vertically is

• 0.314 s

• 3.14 s

• 0.628 s

• 0.157 s

Two simple harmonic motions are represented by ${\mathrm{y}}_1 = 4 \sin (4\mathrm{\pi t} + \mathrm{\pi }/2)$ and ${\mathrm{y}}_2 = 3 \cos \left(4\mathrm{\pi t}\right)$. The resultant amplitude is

• 7

• 1

• 5

• $2 + \sqrt{3}$