If the displacement \(x\) and the velocity \(v\) of a particle executing simple harmonic motion are related through the expression \(4v^2= 25-x^2,\) then its time period will be:

1.	\(\pi \)	2.	\(2 \pi \)
3.	\(4 \pi \)	4.	\(6 \pi\)

A particle of mass 5 gm executing SHM has amplitude of 8 cm. If it makes 16 vibrations per second. Its energy at mean position is

1. $1.6{\mathrm{\pi }}^2\times {10}^5 \mathrm{erg}$

2. $1.6\times {10}^5 \mathrm{erg}$

3. $3.2{\mathrm{\pi }}^2\times {10}^5 \mathrm{erg}$

4. $0.8\times {10}^6 \mathrm{erg}$

The time period of a spring mass system at the surface of the earth is \(2~\text{s}.\) What will be the time period of this system on the moon where the acceleration due to gravity is \(\frac{1}{16}^\text{th}\) of the value of \(g\) on the earth's surface?

A block \(P\) of mass \(m\) is placed on a frictionless horizontal surface. Another block \(Q\) of same mass is kept on \(P\) and connected to the wall with the help of a spring of spring constant \(k\) as shown in the figure. \(\mu_s\) is the coefficient of friction between \(P\) and \(Q\). The blocks move together performing SHM of amplitude \(A\). The maximum value of the friction force between \(P\) and \(Q\) will be:

         
1. \(kA\)
2. \(\frac{kA}{2}\)
3. zero
4. \(\mu_s mg\)

A small sphere carrying a charge ‘q’ is hanging in between two parallel plates by a string of length L. Time period of pendulum is T₀. When parallel plates are charged, the electric field between the plates is E and time period changes to T. The ratio T/T₀ is equal to 

(1) ${\left(\frac{{\displaystyle g+\frac{{\displaystyle qE}}{{\displaystyle m}}}}{{\displaystyle g}}\right)}^{1/2}$           (2) ${\left(\frac{{\displaystyle g}}{{\displaystyle g+\frac{{\displaystyle qE}}{{\displaystyle m}}}}\right)}^{3/2}$

(3) ${\left(\frac{{\displaystyle g}}{{\displaystyle g+\frac{{\displaystyle qE}}{{\displaystyle m}}}}\right)}^{1/2}$           (4) None of these 

A particle is executing a simple harmonic motion. Its maximum acceleration is α and maximum velocity is  β. Then, its time period of vibration will be

1. β²/α² 
 

2. α/β
 

3. β²/α
 

4. 2πβ/α