The period of vibration of a mass m suspended from a spring is 2 s. If along with it  another mass of 2 kg is also suspended, the period of oscillation increases by ls. The mass m will be

• 2 kg

• 1 kg

• 1.6 kg

• 2.6 kg

If length of a simple pendulum increases by 300%, then its time period increases by

• 100 %

• 200 %

• 300 %

• 400 %

Potential energy of a particle at a distance x from mean position, which is executing simple harmonic motion

• $\frac{1}{2} {\mathrm{m\omega }}^2{\mathrm{x}}^2$

• zero

• ${\mathrm{m}}^2\mathrm{\omega x}$

• $\frac{1}{2} {\mathrm{m}}^2{\mathrm{\omega }}^2{\mathrm{x}}^2$

224.

A body executes simple harmonic motion under the action of force F₁ with a time period $\frac{4}{5}$s. If the force is changed to F₂ it executes simple harmonic motion with time period $\frac{3}{5} \mathrm{s}$.If both forces F₁ and F₂ act simultaneously in the same direction on the body, its time period will be

• $\frac{12}{25} \mathrm{s}$

• $\frac{24}{25} \mathrm{s}$

• $\frac{35}{24} \mathrm{s}$

• $\frac{15}{12} \mathrm{s}$

A man measure time period of a pendulum (T) in stationary lift. If the lift moves upward with acceleration g /4, then new time period will be

• $\sqrt{\frac{2}{5}} \mathrm{T}$

• $\sqrt{\frac{5}{2}} \mathrm{T}$

• $\frac{\sqrt{5 }\mathrm{T}}{2}$

• $\frac{2 \mathrm{T}}{\sqrt{5}}$

A mass m is suspended from the two springs ofspring constants k₁ and k₂ as shown. The time period of vertical oscillations of the mass will be

• $2\mathrm{\pi }\sqrt{\left(\frac{{\mathrm{k}}_1 + {\mathrm{k}}_2}{\mathrm{m}}\right)}$

• $2\mathrm{\pi } \sqrt{\left(\frac{\mathrm{m}}{{\mathrm{k}}_1 + {\mathrm{k}}_2}\right)}$

• $2\mathrm{\pi }\sqrt{\frac{\mathrm{m} \left({\mathrm{k}}_1 {\mathrm{k}}_2\right)}{{\mathrm{k}}_1 + {\mathrm{k}}_2}}$

• $2\mathrm{\pi }\sqrt{\frac{\mathrm{m} \left({\mathrm{k}}_1 + {\mathrm{k}}_2\right)}{\left({\mathrm{k}}_1 {\mathrm{k}}_2\right)}}$

A simple pendulum of length l has a maximum angular displacement Q. The maximum kinetic energy of the bob is

• mgl (1 - cosθ)

• 0.5 mgl

• mgl

• 2 mgl

A lift is ascending with an acceleration $\frac{\mathrm{g}}{3}$ . A simple pendulum suspended from its ceiling oscillates with a period T. The period of oscillation of pendulum when the lift is stationary will be

• $\frac{1}{\sqrt{3}} \mathrm{T}$

• T

• 2 T

• $\frac{2}{\sqrt{3}} \mathrm{T}$

A particle executes SHM of amplitude 4 cm and time period 2 s. Then, the time taken by it to move from positive extreme position to half the amplitude is

• $\frac{1}{3} \mathrm{s}$

• $\frac{1}{2} \mathrm{s}$

• $\frac{1}{4} \mathrm{s}$

• 2 s

An organ pipe open at one end is vibrating in second harmonic and is in resonance with another pipe open at both the ends and vibrating in second overtone. The ratio of length of two pipes is

• $\frac{1}{2}$

• $\frac{1}{4}$

• $\frac{3}{4}$

• $\frac{3}{2}$