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The maximum velocity of a particle performing linear S.H.M. is 0.16 m/s. If its maximum acceleration is 0.64 m/s2, calculate its period.
Concept: Differential Equation of Linear S.H.M.
The average displacement over a period of S.H.M. is ______.
(A = amplitude of S.H.M.)
Concept: Simple Harmonic Motion (S.H.M.)
Define phase of S.H.M.
Concept: Simple Harmonic Motion (S.H.M.)
The number of degrees of freedom for a rigid diatomic molecule is.................
(a) 3
(b) 5
(c) 6
(d) 7
Concept: Projection of U.C.M.(Uniform Circular Motion) on Any Diameter
Two particles perform linear simple harmonic motion along the same path of length 2A and period T as shown in the graph below. The phase difference between them is ___________.
Concept: Differential Equation of Linear S.H.M.
Calculate the kinetic energy of 10 gram of Argon molecules at 127°C.
[Universal gas constant R = 8320 J/k mole K. Atomic weight of Argon = 40]
Concept: Phase of K.E (Kinetic Energy)
A copper metal cube has each side of length 1 m. The bottom edge of the cube is fixed and tangential force 4.2x108 N is applied to a top surface. Calculate the lateral displacement of the top surface if modulus of rigidity of copper is 14x1010 N/m2.
Concept: Periodic and Oscillatory Motion
State an expression for K. E. (kinetic energy) and P. E. (potential energy) at displacement ‘x’ for a particle performing linear S.H. M. Represent them graphically. Find the displacement at which K. E. is equal to P. E.
Concept: K.E.(Kinetic Energy) and P.E.(Potential Energy) in S.H.M.
When the length of a simple pendulum is decreased by 20 cm, the period changes by 10%. Find the original length of the pendulum.
Concept: Some Systems Executing Simple Harmonic Motion
The phase difference between displacement and acceleration of a particle performing S.H.M. is _______.
(A) `pi/2rad`
(B) π rad
(C) 2π rad
(D)`(3pi)/2rad`
Concept: Some Systems Executing Simple Harmonic Motion
In a damped harmonic oscillator, periodic oscillations have _______ amplitude.
(A) gradually increasing
(B) suddenly increasing
(C) suddenly decreasing
(D) gradually decreasing
Concept: Simple Harmonic Motion (S.H.M.)
Prove the law of conservation of energy for a particle performing simple harmonic motion.Hence graphically show the variation of kinetic energy and potential energy w. r. t. instantaneous displacement.
Concept: K.E.(Kinetic Energy) and P.E.(Potential Energy) in S.H.M.
Assuming the expression for displacement of a particle starting from extreme position, explain graphically the variation of velocity and acceleration w.r.t. time.
Concept: Simple Harmonic Motion (S.H.M.)
A clock regulated by seconds pendulum, keeps correct time. During summer, length of pendulum increases to 1.005 m. How much will the clock gain or loose in one day?
(g = 9.8 m/s2 and π = 3.142)
Concept: Some Systems Executing Simple Harmonic Motion
A particle executes S.H.M. with a period of 10 seconds. Find the time in which its potential energy will be half of its total energy.
Concept: Simple Harmonic Motion (S.H.M.)
Define practical simple pendulum
Concept: Some Systems Executing Simple Harmonic Motion
Answer in brief:
Derive an expression for the period of motion of a simple pendulum. On which factors does it depend?
Concept: Periodic and Oscillatory Motion
The kinetic energy of nitrogen per unit mass at 300 K is 2.5 × 106 J/kg. Find the kinetic energy of 4 kg oxygen at 600 K. (Molecular weight of nitrogen = 28, Molecular weight of oxygen = 32)
Concept: K.E.(Kinetic Energy) and P.E.(Potential Energy) in S.H.M.
A body of mass 1 kg is made to oscillate on a spring of force constant 16 N/m. Calculate:
a) Angular frequency
b) frequency of vibration.
Concept: Simple Harmonic Motion (S.H.M.)
A particle executing linear S.H.M. has velocities v1 and v2 at distances x1 and x2 respectively from the mean position. The angular velocity of the particle is _______
Concept: Differential Equation of Linear S.H.M.
