Podcast
Questions and Answers
What is the period of a simple harmonic motion with a frequency of 0.955 Hz?
What is the period of a simple harmonic motion with a frequency of 0.955 Hz?
The potential energy of a particle performing linear S.H.M. is proportional to its displacement squared.
The potential energy of a particle performing linear S.H.M. is proportional to its displacement squared.
True
What is the restoring force acting on a bob of mass 50 g displaced by 3 cm in simple harmonic motion?
What is the restoring force acting on a bob of mass 50 g displaced by 3 cm in simple harmonic motion?
1.48 × 10⁻² N
The kinetic energy of a particle performing S.H.M. is ______ when the particle is at the mean position.
The kinetic energy of a particle performing S.H.M. is ______ when the particle is at the mean position.
Signup and view all the answers
Match the following values with their corresponding S.H.M. concepts:
Match the following values with their corresponding S.H.M. concepts:
Signup and view all the answers
The total energy of a body performing S.H.M. with mass 2 kg is 40 J. What is its speed while crossing the center of the path?
The total energy of a body performing S.H.M. with mass 2 kg is 40 J. What is its speed while crossing the center of the path?
Signup and view all the answers
A simple pendulum's displacement is always maximum at the mean position.
A simple pendulum's displacement is always maximum at the mean position.
Signup and view all the answers
What is the frequency of S.H.M. if the potential energy is given as 0.1π²x² joules and the mass of the particle is 20 g?
What is the frequency of S.H.M. if the potential energy is given as 0.1π²x² joules and the mass of the particle is 20 g?
Signup and view all the answers
The change in length of a second's pendulum due to a change in acceleration due to gravity is found to be ______ m.
The change in length of a second's pendulum due to a change in acceleration due to gravity is found to be ______ m.
Signup and view all the answers
How much time after crossing the mean position will the displacement of the bob be one third of its amplitude for a pendulum with a period of 4 seconds?
How much time after crossing the mean position will the displacement of the bob be one third of its amplitude for a pendulum with a period of 4 seconds?
Signup and view all the answers
A particle performs linear S.H.M. starting from the mean position. At the instance when its speed is half the maximum speed, what is the displacement x?
A particle performs linear S.H.M. starting from the mean position. At the instance when its speed is half the maximum speed, what is the displacement x?
Signup and view all the answers
The maximum kinetic energy of a body performing S.H.M. can be calculated from its amplitude and frequency.
The maximum kinetic energy of a body performing S.H.M. can be calculated from its amplitude and frequency.
Signup and view all the answers
What is the period of a pendulum on the moon if the length of the second's pendulum on earth is nearly 1 m?
What is the period of a pendulum on the moon if the length of the second's pendulum on earth is nearly 1 m?
Signup and view all the answers
The maximum frequency possible for a block on a vibrating piston with an amplitude of 25 cm is _____ Hz.
The maximum frequency possible for a block on a vibrating piston with an amplitude of 25 cm is _____ Hz.
Signup and view all the answers
Match the following parameters in linear S.H.M. with their corresponding formulas:
Match the following parameters in linear S.H.M. with their corresponding formulas:
Signup and view all the answers
What is the maximum kinetic energy of a body with the equation of motion x = 6 sin(100t + π/4)?
What is the maximum kinetic energy of a body with the equation of motion x = 6 sin(100t + π/4)?
Signup and view all the answers
The frequency of vertical oscillations for springs in series is higher than for springs in parallel.
The frequency of vertical oscillations for springs in series is higher than for springs in parallel.
Signup and view all the answers
How many oscillations per minute does a magnet vibrating in a uniform field of 1.6 × 10⁻⁵ Wb/m² perform if its moment of inertia is 3 × 10⁻⁶ kg/m²?
How many oscillations per minute does a magnet vibrating in a uniform field of 1.6 × 10⁻⁵ Wb/m² perform if its moment of inertia is 3 × 10⁻⁶ kg/m²?
Signup and view all the answers
The energy per unit mass of the block when the maximum frequency is _____ is 1.25 J/kg.
The energy per unit mass of the block when the maximum frequency is _____ is 1.25 J/kg.
Signup and view all the answers
Which of the following statements is correct regarding the graph of displacement in S.H.M.?
Which of the following statements is correct regarding the graph of displacement in S.H.M.?
Signup and view all the answers
Study Notes
Simple Harmonic Motion (SHM)
-
SHM is a type of oscillatory motion where the restoring force is directly proportional to the displacement from the equilibrium position.
-
The differential equation for SHM in SI units is d²x/dt² = -36x.
-
Frequency (f) and period (T) are related by f = 1/T.
Properties of SHM
-
The maximum displacement from the equilibrium position is called the amplitude.
-
The time taken for one complete oscillation is the period.
-
The number of oscillations per unit time is the frequency.
-
The acceleration of an object undergoing SHM is always directed towards the equilibrium position.
Potential Energy in SHM
-
Potential energy (PE) is expressed as 0.1 π²x² Joules.
-
Mass (m) and frequency (f) are related: f = √(k/m).
-
Amplitude (A). x = A sin(ωt + φ) where ω is angular frequency.
Total Energy
-
Total energy (E) is the sum of kinetic energy (KE) and potential energy (PE).
-
The total energy (E) of a body in SHM with mass (m) is 40J.
-
Speed while crossing the centre of the path is 6.324 cm/s.
Time and Displacement in Simple Pendulum
-
A simple pendulum performs SHM with a period (T) of 4 seconds.
-
Time (t) after crossing the mean position for displacement equal to (1/3)amplitude = 0.2163 seconds.
Simple Pendulum Restoring Force
-
Restoring force in SHM (when length = 1m) = 1.48 × 10⁻² N.
-
Restoring force depends on the displacement from the mean position.
Change in Length of Second's Pendulum
- Change in length of a second's pendulum (due to change in acceleration due to gravity) = 0.0051 m .
Kinetic and Potential Energies
-
Kinetic energy is three times the potential energy at a distance of 4 cm from mean position (amplitude = 8 cm).
-
Potential Energy is proportional to square of displacement from mean position.
-
Kinetic energy is maximum at mean position.
-
Total energy of particle performing SHM remains constant.
Oscillations of a Body Mass
-
T = 2π √(m/k), where T = Period, m = mass and k = spring constant.
-
Comparing masses of oscillators: m₁/(m₂)= 1/3
Superposition of SHMs
-
Two SHMs with x₁ = 5sin (4πt + π/3) cm and x₂ = 3sin(4πt + π/4) cm can be superposed.
-
Resultant amplitude = 7.936 cm and epoch = 54° 23′ .
Coupled Oscillations
-
A circular disc with mass (200 g ) suspended and twisted by 60° will perform angular SHM.
-
Maximum restoring torque is 0.04133 Nm.
Magnet Oscillations in Magnetic Field
- A magnet oscillating in a 1.6 x 10⁻⁵ Wb/m² uniform field oscillates with period 38.19 osc/min.
Block Vibrating on Piston
-
A block of mass (m) on a piston vibrating at maximum frequency and amplitude 25 cm will not leave the piston if the frequency is less than certain value.
-
Maximum energy per unit mass is 1.25 J/kg.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Related Documents
Description
Test your knowledge on Simple Harmonic Motion (SHM) through this quiz. Explore key concepts such as amplitude, frequency, potential energy, and the differential equations governing SHM. Ideal for students learning about oscillatory motion in physics.
