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A particle executing simple harmonic motion with amplitude of $0.1 \,m$. At a certain instant when its displacement is $0.02 \,m$, its acceleration is $0.5 \,m/s^2$. The maximum velocity of the particle is (in $m/s$)
For a simple pendulum, a graph is plotted between its kinetic energy $(KE)$ and potential energy $(PE)$ against its displacement $d$. Which one of the following represents these correctly? (graphs are schematic and not drawn to scale)
When a body of mass $1.0\, kg$ is suspended from a certain light spring hanging vertically, its length increases by $5\, cm$. By suspending $2.0\, kg$ block to the spring and if the block is pulled through $10\, cm$ and released the maximum velocity in it in $m/s$ is : (Acceleration due to gravity $ = 10\,m/{s^2})$
Time 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 :
An assembly of identical spring-mass systems is placed on a smooth horizontal surface as shown. Initially the springs are relaxed. The left mass is displaced to the left while the right mass is displaced to the right and released. The resulting collision is elastic. The time period of the oscillations of the system is :-
A particle is executing simple harmonic motion $(SHM)$ of amplitude $A,$ along the $x-$ axis, about $x = 0.$ When its potential energy $(PE)$ equals kinetic energy $(KE),$ the position of the particle will be