The angular velocity and the amplitude of a simple pendulum is $'\omega '$ and $'A'$ respectively. At a displacement $x$ from the mean position its kinetic energy is $'T'$ and potnetial energy is $'V'$. Then the ratio $\frac{V}{T}$ is
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The period of oscillation of a mass $M$ suspended from a spring of negligible mass is $T$. If along with it another mass $M$ is also suspended , the period of oscillation will now be
A system of two identical rods ($L-$ shaped) of mass $m$ and length $l$ are resting on a peg $P$ as shown in the figure. If the system is displaced in its plane by a small angle $\theta ,$ find the period of oscillations :
A particle moves with simple harmonic motion in a straight line. In first $\tau \,s,$ after starting from rest it travels a distance $a,$ and in next $\tau \,s$ it travels $2a,$ in same direction, then
A particle of mass $5 × 10^{-5}\ kg$ is placed at lowest point of smooth parabola $x^2 = 40y$ ( $x$ and $y$ in $m$ ). If it is displaced slightly such that it is constrained to move along parabola, angular frequency of oscillation (in $rad/s$) will be approximately:-
A mass $m$ is vertically suspended from a spring of negligible mass; the system oscillates with a frequency $n$. What will be the frequency of the system if a mass $4 m$ is suspended from the same spring
Two identical springs have the same force constant $73.5 \,Nm ^{-1}$. The elongation produced in each spring in three cases shown in Figure-$1$, Figure-$2$ and Figure-$3$ are $\left(g=9.8 \,ms ^{-2}\right)$
A body executing $S.H.M.$ along a straightline has a velocity of $3 \,ms ^{-1}$ when it is at a distance of $4 \,m$ from its mean position and $4 \,ms ^{-1}$ when it is at a distance of $3 \,m$ from its mean position. Its angular frequency and amplitude are
A second's pendulum is placed in a space laboratory orbiting around the earth at a height $3R$, where $R$ is the radius of the earth. The time period of the pendulum is