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The equation of S.H.M of a particle is is a positive constant. The time period of motion is given by :
Compare with equation of SHM of the particle with the standard equation
If length of simple pendulum is increased by 6 % then percentage change in time period will be :
A particle is executing S.H.M. from mean position at 5 cm distance, acceleration is 20 cm/s^{2} then value of angular velocity will be :
The relation between the acceleration and angular velocity is as follows:
a = ω^{2}x
ω = √a/x
Substituting value of a and x in the above equation:
ω = 2 rad/s.
The correct answer is: 2 rad/s
A man measures the period of a simple pendulum inside a stationary lift and finds it to be T sec. If the lift accelerates upwards with an acceleration then the period of the pendulum will be :
The maximum velocity of harmonic oscillator is a, and its maximum acceleration is β Its time period will be :
One mass m is suspended from a spring. Time period of oscillation is T. Now if spring is divided into n piece and these are joined in parallel order then time period of oscillation if same mass is suspended.
K_{eq} = n^{2}k is correct but it is a 2 step process
First, K’ = k x n as the spring constant becomes ‘n’ times due to shortening of length
Second, K_{eq} = n x K’ as they are connected in a parallel manner
=>K_{eq} = n^{2}K
Amplitude of harmonic oscillator is a when velocity of particle is half of maximum velocity, then position of particle will be :
A simple pendulum suspended from the ceiling of a stationary trolley has a length Its period of oscillation is What will be its period of oscillation if the trolley moves forward with an acceleration f ?
The value of time period is when the only force acting on the pendulum is mg its weight and its acceleration is g as shown in the picture below.
Now when the trolly is accelerating with force, f, then the resultant acceleration of the pendulum is
It is depicted in the diagram below.
Then the resultant time period will be
In S.H.M, the graph between kinetic energy 'K' and time 't' is:
The correct answer is:
The kinetic energy is KE= ½mv^{2},where m is the mass of the pendulum, and v is the speed of the pendulum.
At the highest pointof the pendulum, it is momentarily motionless. All of the energy in the pendulum is gravitational potential energy and there is no kinetic energy. At the lowest point the pendulum has its greatest speed. All of the energy in the pendulum is kinetic energy and there is no gravitational potential energy. This perioic motion continues, hence the graph will be the one shown in the picture.
Two object A and B of equal mass are suspended from two springs of spring constants K_{A} and K_{B} if the objects oscillate vertically in such a manner that their maximum kinetic energies are equal, then the ratio of their amplitude is :
Kinetic energy of A = Kinetic energy of B.
So, ratio of amplitude
The correct answer is:
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