The natural angular frequency of a particle of mass 'm' attached to an ideal spring of force constant 'K' is

Spring in vehicles are introduces to:

A block of mass m is hanging vertically by spring of spring constant k. If the mass is made to oscillate vertically, its total energy is:

If two springs of spring constant $k _1$ and $k _2$ are connected together in parallel, the effective spring constant will be

A block of mass m is suspended separately by two different springs have time period ${ t } _{ 1 }$ and ${ t } _{ 2 }$. If same mass is connected to parallel combination of both springs, then its time period is $T$. Then

Springs of spring constants K, 2K, 4K, 8K, 2048 K are connected in series. A mass 'm' is attached to one end the system is allowed to oscillation. The time period is approximately :

A body of mass $m$ has time period $T _1$ with one spring and has time period $T _2$ with another spring. if both the spring are connected in parallel and same mass is used, then new time period $T$ is given as

When two blocks A and B coupled by a spring on a frictionless table are stretched and then released, then

Two blocks of masses $m _1$ and $m _2$ are connected by a massless spring and placed on smooth surface. The spring initially stretched and released. Then:

Two masses $m _{1}=1\ kg$ and $m _{2}=0.5\ kg$ are suspended together by a massless spring of spring constant $12.5\ Nm^{-1}$. When masses are in  equilibrium $m _{1}$ is removed without disturbing the system. New amplitude of oscillation will be 

A mass of 10g is connected to a massless spring then time period of small oscillation is 10 second. If 10 g mass is replaced by 40 g mass in same spring then its time period will be :-

Two equal masses are connected by a spring satisfying Hooks law and are placed on a frictionless table. The spring is elongated a little and allowed to go. Let the angular frequency of oscillations be $\omega$. Now one of the masses is stopped. The square of the new angular frequency is :

The springs of force constants $K, 2K, 4K, 8K,....128K$ are connected vertically in series and a body of mass M is suspended from the last spring. If this system is set into oscillations, the time period will be- 

A spring is placed in vertical position by suspending it from a hook at its top. A similar hook on the bottom of the spring is at $11\ cm$ above a table top. A mass of $75\ g$ and of negligible size is then suspended from the bottom hook, which is measured to be $4.5\ cm$ above the table top. The mass is then pulled down a distance of $4\ cm$ and released. Find the approximate position of the bottom hook after $s$?
Take $g=10m/{s}^{2}$ and hooks mass to be negligible.

A block of mass m moving with speed v compresses a spring through distance X before its speed is halved.What is the value of spring constant?

A spring executes SHM with mass of 10 kg attached to it. The force constant of spring is 10 N/m.If at any instant its velocity is 40 cm/sec. The displacement will be (here amplitude is0.5m) 

Two identical springs are fixed at one end and masses 1$\mathrm { kg }$ and 4$\mathrm { kg }$ are suspended at their other ends. Theyare both stretched down from their mean position and let go simultaneously. If they are in the same phase atter every 4 seconds then the springs constant $\mathrm { k }$ is 

A spring mass system is hanging from the ceiling of an elevator in equilibrium. The elevator suddenly starts accelerating upwards with accelerating a, consider all the options in the reference frame of elevator. 

The reading of a spring balance when a block is suspended from it in air is $60 N$. The reading is changed to $40 N$ when the block is submerged in water. The specific gravity of the block must be therefore.

A block of mass $1$ kg is connected to a spring of spring constant $\pi^2 N/m$ fixed at other end and kept on smooth level ground. The block is pulled by a distance of $1$ cm from natural length position and released. After what time does the block compress the spring by $\frac{1}{2} cm$.

A spring (of spring constant $= k )$ is cut into 4 equal parts and two parts are connected in parallel. What is the effective spring constant of these parts?

A man of mass 50 kg stands on the horizontal platform of a spring balance. The platform starts oscillating with amplitude 0.1 m and frequency $2/  \pi$ Hz. The reading of the spring balance will fluctuate between

A spring of force constant k rests on asmooth floor, with one end fixed to awall. A block of mass $m$ hits the free end of the spring with velocity $v$ . Themaximum force exerted by the springon the wall is 

A body of mass 100 gm is suspended from a spring of force constant 50 N/m. The maximum acceleration produced in the spring is:

Two springs mass systems having equal mass and spring constant ${k} _{1}$ and ${k} _{2}$. If the maximum velocities in two systems are equal then ratio of amplitude of 1st so that of 2nd is

Two bodies A and B of equal mass are suspended from two spearte massless springs of spring contnat ${ K } _{ 1 }$ and  respectively If the bodies oscillate vertically such that their maximum velocities are ewqual , the ratio of the amplitude of A to that of B is 

Three masses 700 gm, 500 gm and 400 gm are suspended at the end of the spring and they are in equilibrium. When the 700 gm mass is removed, the system oscillates with a period of 3 sec, when the 500 gm mass is also removed, it will oscillate with a period of 

A uniform spring of force constant $k$ is cut into pieces whose length are in the ratio $1 : 2$. What is the force constant of second piece in terms of $k$?

The spring constant of a spring is $K$. When it is divided into n equal parts, then what is the spring constant of one piece :

Two blocks m and m each of mass 3kg is connected with spring of constant 50 N/m. The coefficient of friction between m and ground is 0.4. The maximum amplitude of m during its oscillation, so that m does not move, is 

A body of mass 'm' when hung from  a long and light spring, the spring stretches by 20 cm The period of vibration of the mass when pulled down the released is 

A sphere of mass 1 kg is connected to a spring of spring constant $ 5.0 Nm^{-1} $ as shown in figure. A force of 0.5 N is applied on the sphere along X-axis , what is the velocity of the sphere when it is displaced througha distance of 10 cm along X-axis?

A spring of length $'l'$ has spring constant $'k'$ is cut into two parts of length $l _{1}$ and $l _{2}$. If their respective spring constants are $k _{1}$ and $k _{2}$, then $\dfrac {k _{1}}{k _{2}}$ is

A block falls from a table $0.6m$ high. It lands on an ideal, mass-less, vertical spring with a force constant of $2.4kN/m$. The spring is initially $25cm$ high, but it is compressed to a minimum height of $10cm$ before the block is stopped. Find the mass of the block $(g=9.81m/s^2)$.

A block of mass $m=4$ kg undergoes simple harmonic motion with amplitude $A=6$ cm on the frictionless surface. Block is attached to a spring of force constant $k=400 N/m$. If the block is at $x = 6$ cm at time $t = 0$ and equilibrium position is at $x=0$ then the blocks position as a function of time (with $x$ in centimetres and $t$ in seconds)?

When a spring-mass system vibrates with simple harmonic motion, the mass in motion reaches its maximum velocity:

A block is attached to an ideal spring undergoes simple harmonic oscillations of amplitude A. Maximum speed of block is calculated at the end of the spring. If the block is replaced by one with twice the mass but the amplitude of its oscillations remains the same, then the maximum speed of the block will

A block of mass $m$ attached to an ideal spring undergoes simple harmonic motion. The acceleration of the block has its maximum magnitude at the point where :

An oscillator consists of a block attached to a spring (k = 400 N/m). At some time t, the position (measured from the system's equilibrium location), velocity and acceleration of the block are x = 0.100m, v = 13.6 m/s, and a = 123 m/s$^2$. The amplitude of the motion and the mass of the block are

A spring balance together with a suspended weight of $2.5$kg is dropped from a height of $30$ metres. The reading on the spring balance, while falling, will show a weight of.

When a Spring of constant K  is cut into 2 equal parts then new spring constant of both the parts would be:

Two identical particles each of mass $0.5\ kg$ are interconnected by a light spring of stiffness $100\ N/m,$ time period of small oscillation is

A $100  g$ mass stretches a particular spring by $9.8\ cm,$ when suspended vertically from it. How large a mass must be attached to the spring if the period of vibration is to be $6.28\ s$?

Two spring-mass systems support equal mass and have spring constants $\displaystyle K _{1}$ and $\displaystyle K _{2}$. If the maximum velocities in two systems are equal then ratio of amplitude of 1st to that of 2nd is 

In the above question, the velocity of the rear 2 kg block after it separates from the spring will be :

A block of mass $200$ g executing SHM under the influence of a spring of spring constant $k = 90 N m^{-1}$ and a damping constant $b = 40 g s^{-1}$. Time taken for its amplitude of vibrations to drop to half of its initial values (Given, In $(1/2) = -0.693)$