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A $3\ kg$ sphere dropped through air has a terminal speed of $25\ m/s$. (Assume that the drag force is $-bv$.) Now suppose the sphere is attached to a spring of force constant $k = 300\ N/m$, and that it oscillates with an initial amplitude of $20\ cm$. What is the angular frequencu of its damped $SHM$? ..... $rad/s$
A mass of $5\, {kg}$ is connected to a spring. The potential energy curve of the simple harmonic motion executed by the system is shown in the figure. A simple pendulum of length $4\, {m}$ has the same period of oscillation as the spring system. What is the value of acceleration due to gravity on the planet where these experiments are performed? (In ${m} / {s}^{2}$)
A large horizontal surface moves up and down in $S.H.M.$ with an amplitude of $1\, cm$. If a mass of $10\, kg$ (which is placed on the surface is to remain continuously in contact with it, the maximum frequency of $S.H.M.$ will be .... $Hz$
A pendulum suspended from the ceiling of a train oscillates with a time period $2$ $second$ , when the train is accelerating at $10\,ms^{-2}$. What will be its time period when the train retards at $10\,ms^{-2}$ ? .... $s$
Two identical spring of constant $K$ are connected in series and parallel as shown in figure. A mass $m$ is suspended from them. The ratio of their frequencies of vertical oscillations will be
A coin is placed on a horizontal platform which undergoes vertical simple harmonic motion of angular frequency $\omega $. The amplitude of oscillation is gradually increased. The coin will leave contact with the platform for the first time
A bob of mass $'m'$ suspended by a thread of length $l$ undergoes simple harmonic oscillations with time period ${T}$. If the bob is immersed in a liquid that has density $\frac{1}{4}$ times that of the bob and the length of the thread is increased by $1 / 3^{\text {rd }}$ of the original length, then the time period of the simple harmonic oscillations will be :-
Two masses $m_1$ and $m_2$ connected by a spring of spring constant $k$ rest on a frictionless surface. If the masses are pulled apart and let go, the time period of oscillation is