Simple Harmonic Motion Problems And Solutions PdfBy Lilp In and pdf 24.04.2021 at 07:30 10 min read
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- 15.2: Simple Harmonic Motion
You might need help with this one so we'll do it all together. This is a self designed lab, and one of the few full write ups in our course.
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Multiple Choice with ONE correct answer 1. The period of oscillation of a simple pendulum of length L suspended from the roof of a vehicle which moves without friction down an inclined plane of inclination a is given by [ marks] Ans. Option a represents the correct answer. Infact, velocity of particle goes on decreasing from maximum value to zero as, the particle travels from mean position to extreme position. A block B is attached to two unstretched springs Sj and S 2 with spring constants k and 4k, respectively see figure 1.
The springs and supports have negligible mass. There is no friction anywhere. The block B is displaced towards wall 1 by a small distance x figure II and released. The block returns and moves a maximum distance y towards wall 2. Displacements x and y are measured with respect to the equilibrium position of the block B.
And when the block B is displaced to the left. The spring S, will have no tension, it will be in its natural length. The x-t graph of a particle undergoing simple harmonic motion is shown below.
The mass M shown in the figure oscillates in simple harmonic motion with amplitude A. A wooden block performs SHM on a frictionless surface with frequency, v 0.
A particle executes simple harmonic motion with a frequency f. It becomes 2f. Frequency of oscillation of K. When the cylinder is given a small downward push and released it starts oscillating vertically with small amplitude.
If the force constant of the spring is k, the frequency of oscillation of the cylinder is [ marks] Ans. A highly rigid cubical block A of small mass M and side L is fixed rigidly onto another cubical block B of the same dimensions and of low modulus of rigidity n such that the lower face of A completely covers the upper face of B.
The lower face of B is rigidly held on a horizontal surface. A small force F is applied perpendicular to one of the side faces of A. After the force is withdrawn, block A executes small oscillations, the time period of which is given by [ marks] Ans.
They have same dimensions. The lower face of B is held rigidly or a horizontal surface. A force F is applied to the upper cube A at right angles to one of the side faces.
The block A executes SHM when the force is withdrawn. The lower block gets distorted. One end of a long metallic wire of length Lis tied to the ceiling. The other end is tied to a massless spring 6f spring constant k. A mass m hangs freely from the free end of the spring. If the mass is slightly pulled down and released, it will oscillate with a time Ans. A particle of mass m is executing osciftations about the origin on the x-axis.
Consider two ways the disc is attached; case A the disc is not free to rotate about its center and case B the disc is free to rotate about its center. The rod — disc system performs SHM in vertical plane after being released from the same displaced position. Which of the following statement s is are true? Comprehension based question For periodic motion of small amplitude A, the time period T of this particle is proportional to Ans. They are especially useful in studying the changes in motion as initial position and momentum are changed.
Here we consider some simple dynamical systems in one-dimension. The phase space diagram is x t vs. The arrow on the curve indicates the time flow. For example, the phase space diagram for a particle moving with constant velocity is a straight line as shown in the figure. We use the sign convention in which position or momentum upwards or to right is positive and downwards or to left is negative Ans. The phase spacem diagram for a ball thrown vertically up from ground is Ans.
After, it become zero and then negative. The phase space diagram for simple harmonic motion is a circle centrred at the origin. In the figure, the two circles represent the same oscillator but for different initial conditions, and E1 and E 2 are the total mechanical energies respectively.
Consider the spring — mass system, with the mass submerged in water, as shown in the figure. The phase space diagram for one cycle of this system is Ans. Assuming that the block is initially pulled down and released, its momentum will increases upwards till it reaches the mean position.
A point mass m is suspended at the end of massless wire of length L and cross-sectional area A. A mass M attached to a spring oscillates with a period of 2 sec.
If the mass is increased by 2kg the period increases by one sec. Find the tension in the thread of the pendulum and the angle it makes with the vertical.
Two masses m1 and m 2 are suspended together by a massless spring of spring constant k. Find the angular frequency and amplitude of oscillation of m 2. The piston and the cylinder have equal cross-sectional area A. Atmospheric pressure is P Q , and when the piston is in equilibrium, the volume of the gas is V 0.
The piston is now displaced slightly down from its equilibrium position. Assuming that the system is completely isolated from its surroundings, show that the piston executes simple harmonic motion and find the frequency of oscillation. A particle of mass 0. Show that the motion of the negatively charged particle is approximately simple harmonic.
Calculate the time period of oscillations. Two light springs of force constants kj and k 2 and a block of mass m are in one line AB on a smooth horizontal table such that one ends of each spring is fixed on rigid supports and the other end is free as shown in the figure.
The distance CD between the free ends of the springs is 60 cm. The block moves to right and compresses the spring along DB. The spring offers restoring force and the block comes back to D. A sphere of radius R is half submerged in liquid of density p. If the sphere is slightly pushed down and release, find the frequency of oscillation. Fill in the blanks type After, it become zero and then negative RD Sharma Class 12 Solutions.
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15.2: Simple Harmonic Motion
An object vibrates with a frequency of 5 Hz to rightward and leftward. The object moves from equilibrium point to the maximum displacement at rightward. Determine the time interval required to reach to the maximum displacement at rightward eleven times. Known :. Wanted: The time interval required to reach to the maximum displacement at rightward eleven times. Solution :.
Simple harmonic motion SHM is a special case of motion in a straight line which occurs in several examples in nature. This is an example of a second order differential equation. We can easily check this:. We write the differential equation as. Hence, we have. A particle is moving in simple harmonic motion.
Streaming Video Help. This lecture continues the topic of harmonic motions. Problems are introduced and solved to explore various aspects of oscillation. The second half of the lecture is an introduction to the nature and behavior of waves. Both longitudinal and transverse waves are defined and explained. Sign in.
General Solution of Simple Harmonic Oscillator Equation. The angular frequency for simple harmonic motion is a constant by.
Springs are a classic example of harmonic motion, on Wikipedia you can get a grasp of the basics. Schneider unity pro xl v13 download. Questions 4 - The maximum acceleration of a particle moving with simple harmonic motion is. Additional Problems: 1 Why is simple harmonic motion so common in classical mechanics?
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