A Spring Of Negligible Mass Having A Force Constant k extends By An Amount y when A Mass m is Hung From It. The Mass Is Pulled Down A Little And Released. The System Begins To Execute Simple Harmonic Motion Of Amplitude A And Angular Frequency ω. The Total Energy Of The Mass-spring System Will Be

Why Kaysons ?

Video lectures

Access over 500+ hours of video lectures 24*7, covering complete syllabus for JEE preparation.

Online Support

Practice over 30000+ questions starting from basic level to JEE advance level.

Live Doubt Clearing Session

Ask your doubts live everyday Join our live doubt clearing session conducted by our experts.

National Mock Tests

Give tests to analyze your progress and evaluate where you stand in terms of your JEE preparation.

Organized Learning

Proper planning to complete syllabus is the key to get a decent rank in JEE.

Test Series/Daily assignments

Give tests to analyze your progress and evaluate where you stand in terms of your JEE preparation.



A spring of negligible mass having a force constant k extends by an amount y when a mass m is hung from it. The mass is pulled down a little and released. The system begins to execute simple harmonic motion of amplitude A and angular frequency ω. The total energy of the mass-spring system will be


Correct option is


Let L be the relaxed length of the spring and y the extension produced in it due to force mg so that 

                ky = mg                                          …(i)

The displacement of the mass during oscillation is given by


At the instant when the displacement is x



Taking gravitational PE at the mean position to be zero, 

Gravitational PE at x = – mg x                                       … (v)

Adding (iii), (iv) and (v), we get 

Total energy of mass-spring system 






A body oscillates harmonically with amplitude 0.05 m. At a certain instant of time its displacement is 0.01 m and acceleration is 1.0 ms-2. What is the period of oscillation?


A tuning fork produces 4 beta per second when sounded with sonometer of vibrating length 48cm. It produces 4 beats per second also when the vibrating length is 50cm. What is the frequency of the tuning fork?



The displacement x (in centimetres) of an oscillating particle varies with time t (in seconds) as 


The magnitude of the maximum acceleration of the particle is 


A particle executes SHM of amplitude 25 cm and time periods 3 s. what is the minimum time required for the particle to move between two points located at 12.5 cm on either side of the mean position?


A body executing linear simple harmonic motion has a velocity of 3 cms–1when its displacement is 4 cm and a velocity of 4 cms–1 when its displacement is 3 cm. what is the amplitude of oscillation?  


A particle is executing linear simple harmonic motion of amplitude A. what fraction of the total energy is kinetic when the displacement is half the amplitude?


Two identical strings of a stringed  musical instrument are in unison when stretched with the same tension. When the tension in one string is increased by 1%, the musician hears 4 beats per second. What was the frequency of the note when the string were in unison?


A horizontal platform is executing simple harmonic motion in the vertical direction of frequency v. A block of mass m is placed on the platform. What is the maximum amplitude of the platform so that the block is not detached from it?


A spring stretches by 0.05 m when a mass of 0.5 kg is hung from it. A body of mass 1.0 kg is attached to one of its ends, the other end being fixed to the wall. The body is pulled 0.01 m along a horizontal frictionless surface and released. What is the total energy of the oscillator. Assume the string to have negligible mass and take g = 10 ms–2.  


A spring has a natural length of 50 cm and a force constant of  A body of mass 10 kg is suspended from it and the spring is stretched. If the body is pulled down further stretching the spring to a length of 58 cm and released, it executes simple harmonic motion. What is the net force on the body when it is at its lowermost position of its oscillation? Take g = 10 ms –2.