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- 1A particle is executing $SHM$ about $y=0$ along $y$-axis. Its position at an instant is given by $y=(7 \,m )$ sin( $\pi f)$. Its average velocity for a time interval $0$ to $0.5 \,s$ is ........... $m / s$View Solution
- 2If particle is executing simple harmonic motion with time period $T$, then the time period of its total mechanical energy is ...........View Solution
- 3If a Second's pendulum is moved to a planet where acceleration due to gravity is $4$ times, the length of the second's pendulum on the planet should be made .......... timesView Solution
- 4A mass $M$ is suspended from a spring of negligible mass. The spring is pulled a little and then released so that the mass executes simple harmonic oscillations with a time period $T$. If the mass is increased by m then the time period becomes $\left( {\frac{5}{4}T} \right)$. The ratio of $\frac{m}{{M}}$ isView Solution
- 5Time period of a particle executing $SHM$ is $8\, sec.$ At $t = 0$ it is at the mean position. The ratio of the distance covered by the particle in the $1^{st}$ second to the $2^{nd}$ second is :View Solution
- 6Four simple harmonic vibrations:View Solution
${y_1} = 8\,\cos\, \omega t;\,{y_2} = 4\,\cos \,\left( {\omega t + \frac{\pi }{2}} \right)$ ;
${y_3} = 2\cos \,\left( {\omega t + \pi } \right);\,{y_4} = \,\cos \,\left( {\omega t + \frac{{3\pi }}{2}} \right)$ ,
are superposed on each other. The resulting amplitude and phase are respectively;
- 7Three mass and string system is in equilibrium. When $700\,gm$ mass is removed, then the system oscillates with a period of $3\,seconds$ . When the $500\,gm$ mass is also removed, then what will be new time period for system ..... $\sec$View Solution
- 8Consider two identical cylinders [each of mass $m$ density $\rho _0$ horizontal cross-section area $s$] in equilibrium, partially submerged in two containers filled with liquids of densities $\rho_1$ and $\rho_2$ as shown in figure. Find the period of small oscillations of this system about its equilibrium. Neglect the changes in the level of liquids in the containers. Neglect mass of the strings. acceleration due to gravity is $g$ . ($v$ is volume of each block)View Solution
- 9If displacement $x$ and velocity $v$ are related as $4v^2 = 25 -x^2$ in a $SHM$. Then time Period of given $SHM$ is (Consider $SI\, units$)View Solution
- 10Two springs have spring constants ${K_A}$ and ${K_B}$ and ${K_A} > {K_B}$. The work required to stretch them by same extension will beView Solution