Oscillating Systems

Derive a time period of a spring when it is cut into two equal parts

If two masses $\mathrm{m} \mathrm{and} 2\mathrm{m}$ are suspended from two springs of spring constants $\mathrm{k} \mathrm{amd} 2\mathrm{k}$ as shown in the figure. Find the accelerations of the upper and lower block , if the lower spring is cut.

What will be the effect on the spring constant, if the spring is cut into two halves?

A spring-mass system of mass $\mathrm{M}$oscillates with the time period $\mathrm{T}$. If the mass is increased by $\mathrm{m}$, then the time period becomes $\frac{5\mathrm{T}}{3}$..Determine the ratio $\frac{\mathrm{m}}{\mathrm{M}}$.

Deduce an expression for an oscillating system consists of a vertical spring with a mass

What provides the restoring force for simple harmonic oscillations in Simple pendulum .

Time period of a simple pendulum is $T.$ The time taken to complete $\frac{5}{8}$ oscillations starting from mean position is $\frac{\alpha }{B}T.$ The value of $\alpha$ is _______ .

Two pendulums begin to swing simultaneously. The first pendulum makes nine full oscillations when the other makes seven. The ratio of the lengths of the two pendulums is

A person measures a time period of a simple pendulum inside a stationary lift and finds it to be $T$. If the lift starts accelerating upwards with an acceleration $\left(\frac{g}{3}\right)$, the time period of the pendulum will be

A vertical spring mass system has the same time period as simple pendulum undergoing small oscillations. Now, both of them are put in an elevator going downwards with an acceleration $5 \mathrm{m} {\mathrm{s}}^{-2}$. The ratio of time period of the spring mass system to the time period of the pendulum is (assume that acceleration due to gravity, $g=10 \mathrm{m} {\mathrm{s}}^{-2}$),

A simple pendulum is placed inside a lift which is moving with a uniform acceleration. If the time periods of the pendulum while the lift is moving upwards and downwards are in the ratio $1:2$, then the acceleration of the lift is (acceleration due to gravity, $g=10 \mathrm{m} {\mathrm{s}}^{-2}$),

A cabin is falling freely under gravity, what is the time period of a pendulum attached to its ceiling?

The time period of a simple pendulum inside a stationary lift is $\sqrt{5} \mathrm{s}$. What will be the time period when the lift moves upwards with an acceleration $\frac{g}{4}?$

The length of a pendulum is decreased by $10⁒$. What will be the change in its frequency?

If the length of a simple pendulum is increased by $25\%$, then what is the change in its time period?

The time period of a simple pendulum depends on the 

The time period for small vertical oscillations of a block of mass $\mathrm{m}$ when the masses of the pulleys are negligible and spring constant ${\mathrm{k}}_1$ and ${\mathrm{k}}_2$ is

Two springs of spring constants $k$ each are connected in series, then what is the net spring constant?

A light spring of force constant $8 {\mathrm{Nm}}^{-1}$ is cut into two equal halves and the two are connected in parallel; the equivalent force constant of the system is

A light spring of constant $k$ is cut into two equal parts. The spring constant of each part is