Definitions [3]
Define the frequency of simple harmonic motion.
The number of oscillations produced by the particle per second is called frequency. It is denoted by f. SI unit for frequency is s−1 or hertz (Hz).
Mathematically, frequency is related to the time period by f = `1/"T"`
Define the time period of simple harmonic motion.
Time period: The time period is defined as the time taken by a particle to complete one oscillation. It is usually denoted by T. For one complete revolution, the time taken is t = T, therefore,
`ω"T"` = 2π ⇒ T = `(2π)/ω`
Define linear S.H.M.
Linear S.H.M. is defined as the linear periodic motion of a body in which the restoring force (or acceleration) is always directed towards its mean position and its magnitude is directly proportional to the displacement from the mean position.
Consider a particle ‘P’ moving along the circumference of a circle of radius 'a' and centre O, with uniform angular speed of 'ω' in anticlockwise direction as shown.
Particle P along the circumference of the circle has its projection particle on diameter AB at point M.
Important Questions [43]
- A copper metal cube has each side of length 1 m. The bottom edge of the cube is fixed and tangential force 4.2x10^8 N is applied to a top surface.
- What is the Periodic Time (T) of that Pendulum Which is Suspended in an Elevator Moving with Constant Speed in Downward Direction
- The Periodic Time of a Linear Harmonic Oscillator is 2π Second, with Maximum Displacement of 1 Cm.
- 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.
- 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.
- Derive an Expression for the Period of Motion of a Simple Pendulum. On Which Factors Does It Depend?
- State the Differential Equation of Linear Simple Harmonic Motion.
- The average displacement over a period of S.H.M. is ______. (A = amplitude of S.H.M.)
- Show Variation of Displacement, Velocity and Acceleration with Phase for a Particle Performing Linear S.H.M. Graphically, When It Starts from Extreme Position.
- Define Phase of S.H.M.
- A Body of Mass 1 Kg is Made to Oscillate on a Spring of Force Constant 16 N/M. Calculate: Angular Frequency Frequency of Vibration.
- 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.
- Assuming the Expression for Displacement of A Particle Starting from Extreme Position, Explain Graphically the Variation of Velocity And Acceleration W.R.T. Time.
- In a Damped Harmonic Oscillator, Periodic Oscillations Have___ Amplitude.
- Calculate the Acceleration When It is at 4 Cm from Its Positive Extreme Position.
- Hence Obtain the Expression for Acceleration, Velocity and Displacemetn of a Particle Performing Linear S.H.M.
- Obtain the differential equation of linear simple harmonic motion.
- Define linear S.H.M.
- The Maximum Velocity of a Particle Performing Linear S.H.M. is 0.16 m/s. If Its Maximum Acceleration is 0.64 m/s^2, Calculate Its Period.
- 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
- A Particle Performing Linear S.H.M. Has a Period of 6.28 Seconds and a Pathlength of 20 cm. What is the Velocity When Its Displacement is 6 cm from Mean Position?
- 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
- 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.
- From Differential Equation of Linear S.H.M., Obtain an Expression for Acceleration, Velocity and Displacement of a Particle Performing S.H.M.
- A particle performing Linear S.H.M. has a maximum velocity 25 cm/sand maximum acceleration 100 cm/s2. Find the period of oscillations.
- The Number of Degrees of Freedom for a Rigid Diatomic Molecule is
- Calculate the Kinetic Energy of 10 Gram of Argon Molecules At 127°C.
- The Pressure (P) of an Ideal Gas Having Volume (V) is 2E/3V , Then the Energy E is
- Calculate the Average Molecular Kinetic Energy : (A) per Kilomole, (B) per Kilogram, of Oxygen at 27°C.
- 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
- 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.
- 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.
- 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)
- Obtain an Expression for Potential Energy of a Particle Performing Simple Harmonic Motion. Hence Evaluate the Potential Energy
- 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?
- Define Practical Simple Pendulum
- 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?
- Show That, Under Certain Conditions, Simple Pendulum Performs the Linear Simple Harmonic Motion.
- If the Particle Starts Its Motion from Mean Position, the Phase Difference Between Displacement and Acceleration is ______.
- The period of a conical pendulum in terms of its length (l), semi-vertical angle (θ) and acceleration due to gravity (g) is ______.
- The Phase Difference Between Displacement and Acceleration of a Particle Performing S.H.M. is
- If the Metal Bob of a Simple Pendulum is Replaced by a Wooden Bob of the Same Size, Then What is Effect on Time Period
- When the Length of a Simple Pendulum is Decreased by 20 Cm, the Period Changes by 10%. Find the Original Length of the Pendulum.
Concepts [8]
- Periodic and Oscillatory Motion
- Simple Harmonic Motion (S.H.M.)
- Differential Equation of Linear S.H.M.
- Projection of U.C.M.(Uniform Circular Motion) on Any Diameter
- Phase of K.E (Kinetic Energy)
- K.E.(Kinetic Energy) and P.E.(Potential Energy) in S.H.M.
- Composition of Two S.H.M.’S Having Same Period and Along Same Line
- Some Systems Executing Simple Harmonic Motion
