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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.
Show that motion of bob of the pendulum with small amplitude is linear S.H.M. Hence obtain an expression for its period. What are the factors on which its period depends?
Concept: Some Systems Executing Simple Harmonic Motion
Show variation of displacement, velocity, and acceleration with phase for a particle performing linear S.H.M. graphically, when it starts from the extreme position.
Concept: Simple Harmonic Motion (S.H.M.)
Show that, under certain conditions, simple pendulum performs the linear simple harmonic motion.
Concept: Some Systems Executing Simple Harmonic Motion
If the particle starts its motion from mean position, the phase difference between displacement and acceleration is ______.
Concept: Some Systems Executing Simple Harmonic Motion
A particle performing linear S.H.M. has the maximum velocity of 25 cm/s and maximum acceleration of 100 cm/ m2. Find the amplitude and period of oscillation. (π = 3.142)
Concept: Differential Equation of Linear S.H.M.
State the differential equation of linear simple harmonic motion.
Concept: Simple Harmonic Motion (S.H.M.)
Hence obtain the expression for acceleration, velocity and displacement of a particle performing linear S.H.M.
Concept: Simple Harmonic Motion (S.H.M.)
Calculate the internal energy at 298K for the formation of one mole of ammonia, if the enthalpy change at constant pressure is – 42.0 kJ mol-1.
(Given: R = 8.314 J K-1 mol-1)
Concept: Chemical Thermodynamics and Energetic >> First Law of Thermodynamics
The length of the second’s pendulum in a clock is increased to 4 times its initial length. Calculate the number of oscillations completed by the new pendulum in one minute.
Concept: Periodic and Oscillatory Motion
Obtan an expression for potential energy of a particle performing S.H.M. What is the value of potential energy at (i) Mean position, and (ii) Extreme position
Concept: K.E.(Kinetic Energy) and P.E.(Potential Energy) in S.H.M.
From differential equation of linear S.H.M., obtain an expression for acceleration, velocity and displacement of a particle performing S.H.M.
Concept: Differential Equation of Linear S.H.M.
