Simple Harmonic Motion Questions And Solutions Pdf

simple harmonic motion questions and solutions pdf

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Simple harmonic motion , in physics , repetitive movement back and forth through an equilibrium , or central, position, so that the maximum displacement on one side of this position is equal to the maximum displacement on the other side.

The time interval of each complete vibration is the same. The force responsible for the motion is always directed toward the equilibrium position and is directly proportional to the distance from it.

A specific example of a simple harmonic oscillator is the vibration of a mass attached to a vertical spring , the other end of which is fixed in a ceiling. At either position of maximum displacement, the force is greatest and is directed toward the equilibrium position, the velocity v of the mass is zero, its acceleration is at a maximum, and the mass changes direction. At the equilibrium position, the velocity is at its maximum and the acceleration a has fallen to zero. Simple harmonic motion is characterized by this changing acceleration that always is directed toward the equilibrium position and is proportional to the displacement from the equilibrium position.

Furthermore, the interval of time for each complete vibration is constant and does not depend on the size of the maximum displacement. In some form, therefore, simple harmonic motion is at the heart of timekeeping.

Many physical systems exhibit simple harmonic motion assuming no energy loss : an oscillating pendulum, the electrons in a wire carrying alternating current , the vibrating particles of the medium in a sound wave, and other assemblages involving relatively small oscillations about a position of stable equilibrium.

The motion is called harmonic because musical instruments make such vibrations that in turn cause corresponding sound waves in air.

Musical sounds are actually a combination of many simple harmonic waves corresponding to the many ways in which the vibrating parts of a musical instrument oscillate in sets of superimposed simple harmonic motions, the frequencies of which are multiples of a lowest fundamental frequency.

In fact, any regularly repetitive motion and any wave, no matter how complicated its form, can be treated as the sum of a series of simple harmonic motions or waves, a discovery first published in by the French mathematician Joseph Fourier. Simple harmonic motion Article Additional Info. Print Cite verified Cite. While every effort has been made to follow citation style rules, there may be some discrepancies.

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The Editors of Encyclopaedia Britannica Encyclopaedia Britannica's editors oversee subject areas in which they have extensive knowledge, whether from years of experience gained by working on that content or via study for an advanced degree See Article History. Read More on This Topic. Consider a mass m held in an equilibrium position by springs, as shown in Figure 2A. The mass may be perturbed by displacing it to Get a Britannica Premium subscription and gain access to exclusive content.

Subscribe Now. Learn More in these related Britannica articles:. The mass may be perturbed by displacing it to the right or left. If x is the displacement of the mass from equilibrium Figure 2B , the springs…. This motion, by stretching the spring between the particles, starts to excite the second particle into motion. Gradually the energy of motion passes from the first particle to the second until a point is reached at which the first particle is at….

This occurs whenever the disturbance to the system is countered by a restoring force that is exactly proportional to the degree of disturbance. History at your fingertips. Sign up here to see what happened On This Day , every day in your inbox! Email address. By signing up, you agree to our Privacy Notice. Be on the lookout for your Britannica newsletter to get trusted stories delivered right to your inbox.

AP Physics 1 : Period and Frequency of Harmonic Motion

These solutions for Simple Harmonic Motion are extremely popular among Class 12 Science students for Physics Simple Harmonic Motion Solutions come handy for quickly completing your homework and preparing for exams. As motion is a change in position of an object with respect to time or a reference point, it is not an example of periodic motion. Simple harmonic motion can take place in a non-inertial frame. However, the ratio of the force applied to the displacement cannot be constant because a non-inertial frame has some acceleration with respect to the inertial frame. Therefore, a fictitious force should be added to explain the motion.

Simple harmonic motion

In this Periodic motion the restoring force is directly proportional to the displacement. The object oscillates between two position and Motion is sinusoidal in nature. Linear Simple Harmonic Motion when the object is oscillating along straight line. The restoring force should be proportional to the displacement from the mean position and acting towards means position. Angular Simple Harmonic Motion when the object is oscillating along circular arc.

Simple harmonic motion , in physics , repetitive movement back and forth through an equilibrium , or central, position, so that the maximum displacement on one side of this position is equal to the maximum displacement on the other side. The time interval of each complete vibration is the same.

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The string vibrates around an equilibrium position, and one oscillation is completed when the string starts from the initial position, travels to one of the extreme positions, then to the other extreme position, and returns to its initial position. We define periodic motion to be any motion that repeats itself at regular time intervals, such as exhibited by the guitar string or by a child swinging on a swing. In this section, we study the basic characteristics of oscillations and their mathematical description.

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. In a certain bay, there is a low tide of 6 metres at 1am and a high tide of 10 metres at 8am.

If the period of the pendulum is , what is the length of the string? We have all of these values, allowing us to solve:. The only value we don't have is length. However, we can develop an expression for length from the given information. The second term describes how close the pendulum gets to the height of the top of the pendulum. Therefore, we subtract this value from the lowest point of the pendulum to get the height relative to its lowest point. We can rewrite this as:.

When you pluck a guitar string, the resulting sound has a steady tone and lasts a long time Figure. The string vibrates around an equilibrium position, and one oscillation is completed when the string starts from the initial position, travels to one of the extreme positions, then to the other extreme position, and returns to its initial position. We define periodic motion to be any motion that repeats itself at regular time intervals, such as exhibited by the guitar string or by a child swinging on a swing.

When you pluck a guitar string, the resulting sound has a steady tone and lasts a long time Figure The string vibrates around an equilibrium position, and one oscillation is completed when the string starts from the initial position, travels to one of the extreme positions, then to the other extreme position, and returns to its initial position. We define periodic motion to be any motion that repeats itself at regular time intervals, such as exhibited by the guitar string or by a child swinging on a swing.

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Questions: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Physics Simple Harmonic Motion Solutions. 1. A −kg particle moves as function of time as follows.

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