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Two particles of mass $m$ are constrained to move along two horizontal frictionless rails that make an angle $2\theta $ with respect to each other. They are connected by a spring with spring constant $k$ . The angular frequency of small oscillations for the motion where the two masses always stay parallel to each other (that is the distance between the meeting point of the rails and each particle is equal) is
This is the position time graph of a mass on spring. What can you say about the velocity and force at the instant indicated by dashed line ? (positive direction is to the right)
Time period of a simple pendulum is $T$. The time taken to complete $5 / 8$ oscillations starting from mean position is $\frac{\alpha}{\beta} T$. The value of $\alpha$ is ..... .
Consider two identical springs each of spring constant $k$ and negligible mass compared to the mass $M$ as shown. Fig. $1$ shows one of them and Fig. $2$ shows their series combination. The ratios of time period of oscillation of the two $SHM$ is $\frac{ T _{ b }}{ T _{ a }}=\sqrt{ x },$ where value of $x$ is
Three 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 ..... $\sec$
A plank with a small block on top of it is under going vertical $SHM.$ Its period is $2\, sec.$ The minimum amplitude at which the block will separate from plank is :
When an oscillator completes $100$ oscillations its amplitude reduced to $\frac{1}{3}$ of initial value. What will be its amplitude, when it completes $200$ oscillations?