Resonance is said to be taken place when:
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Resonance occurs when the driving frequency equals the natural frequency.
Wave form of S.H.M is:
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Simple harmonic motion can be represented by a sinusoidal wave.
A force of 20 N is applied on an elastic spring. If the extension produced in the spring is 10 cm, the spring constant of the spring is:
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Use Hooke's law F = kx and convert 10 cm to 0.10 m.
When simple pendulum swings, which of the following quantity does not become zero throughout the oscillation:
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The mass remains constant, while velocity, momentum and acceleration can be zero at particular positions.
The time period of simple pendulum depends upon:
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For small oscillations, T = 2π√(l/g).
Which of the following law remains valid in a vibratory motion (S.H.M)?
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Kinetic and potential energy continuously transform while total energy remains constant in ideal SHM.
The time period of a simple pendulum of length l is given by T = 2π√(l/g). If the length of pendulum is increased by four times its initial length, then the new time period will be:
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The period is proportional to √l; four times the length gives twice the period.
If the mass of a simple pendulum is reduced to half, its time period:
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The period of a simple pendulum is independent of bob mass.
The length of a second's pendulum on the surface of the moon, where g is 1/6 of the value of g on the surface of the earth is:
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For a fixed period, pendulum length is proportional to g.
At extreme position during the vibration of a body executing S.H.M:
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At maximum displacement, velocity is zero and potential energy is maximum.
We can increase the time-period of mass-spring system:
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For a spring-mass system, T = 2π√(m/k).
If a point mass m is moving on a circle of radius x₀ with a constant angular velocity ω, where the period of oscillation is T and the displacement is x, then the kinetic energy of particle at any instant is:
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In SHM, total energy is ½kx₀² and potential energy is ½kx².
The restoring force is directly proportional to the displacement of the system from its equilibrium position, it is called:
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Hooke's law states that restoring force is proportional to displacement within the elastic limit.
In a simple harmonic motion, which of the following does not hold:
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Potential energy is minimum at the mean position and maximum at the extremes.
If a hole is bored along a diameter of the earth and a stone is dropped into the hole it will:
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Inside an idealized Earth, gravitational restoring force is proportional to displacement from the center.
A spring of harmonic oscillator is cut into two equal halves. If the same force is applied on a full and a half spring respectively, then the spring constant of halved spring will:
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For a uniform spring, spring constant is inversely proportional to its length.
A particle of mass 200 g executes S.H.M. The restoring force is provided by a spring of force constant 80 N/m. The time period of oscillation is:
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Use T = 2π√(m/k), with m = 0.2 kg.
When quarter of the cycle is completed by a body in a circular motion, the phase of vibration is:
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One quarter of a cycle corresponds to 90° or π/2 radians.
How long must be the length of a simple pendulum in order to have a period of one second?
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Use T = 2π√(l/g); for T = 1 s, l is approximately 0.25 m.
The time period of simple pendulum is independent from its:
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For small oscillations, the simple pendulum period does not depend on bob mass.
