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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.
A body of mass 1 kg is mafe to oscillate on a spring of force constant 16 N/m. Calculate (a) Angular frequency, (b) Frequency of vibrations.
Concept: Periodic and Oscillatory Motion
During refrigeration cycle, heat is rejected by the refrigerant in the ______.
Concept: Refrigerators and Heat Pumps
Answer in brief:
A gas contained in a cylinder surrounded by a thick layer of insulating material is quickly compressed has work been done?
Concept: Heat Engine
Give an example of some familiar process in which no heat is added to or removed from a system, but the temperature of the system changes.
Concept: Thermodynamics
A gas contained in a cylinder fitted with a frictionless piston expands against a constant external pressure of 1 atm from a volume of 5 liters to a volume of 10 liters. In doing so it absorbs 400J of thermal energy from its surroundings. Determine the change in the internal energy of the system.
Concept: Thermodynamics
A system releases 130 kJ of heat while 109 kJ of work is done on the system. Calculate the change in internal energy.
Concept: Heat, Internal Energy and Work
An ideal monoatomic gas is adiabatically compressed so that its final temperature is twice its initial temperature. What is the ratio of the final pressure to its initial pressure?
Concept: Chemical Thermodynamics and Energetic >> First Law of Thermodynamics
In SI units, the differential equation of an S.H.M. is `(d^2x)/(dt^2)` = − 36x. Find its frequency and period.
Concept: Differential Equation of Linear S.H.M.
