Is the only sufficient or necessary?
As you know, the word “only” introduces the necessary condition of a S&N statement. So, if we have “Only A is B,” A is our necessary condition and B is our sufficient condition.
Which of the following is necessary and sufficient condition for simple harmonic motion?
The frequency represents the number of oscillations that the particle makes per unit time. The acceleration of the particle is proportional to the displacement but is in the opposite direction. This is the necessary and sufficient condition for simple harmonic motion, as opposed to all other kinds of vibration.
What are the conditions of SHM?
Define simple harmonic motion. What are the conditions of SHM?
- There must be an elastic restoring force acting on the system.
- The system must have inertia.
- The acceleration of the system should be directly proportional to its displacement and is always directed to mean position.
Which of the following conditions is not sufficient for simple harmonic motion and why?
Solution : Condition(i) is not sufficient because it gives no reference of the direction of acceleration, where as in SHM the acceleration is always in a direction opposite to that of the displacement .
What is equation of SHM?
Simple Harmonic Motion or SHM is defined as a motion in which the restoring force is directly proportional to the displacement of the body from its mean position. The acceleration of a particle executing simple harmonic motion is given by, a(t) = -ω2 x(t). Here, ω is the angular velocity of the particle.
How do you prove SHM?
For example, let’s say there is mass m mounted between 2 spring with spring constant k1, k2 which are attached to wall and have its original length when system is at equilibrium. When the mass is disturbed slightly by displacement x, the restoring force will be F=−(k2+k1)x which proves the motion will be SHM.
What is SHM and its characteristics?
Following are the main characteristics of simple harmonic motion: In simple harmonic motion, the acceleration of the particle is directly proportional to its displacement and directed towards its mean position. The total energy of the particle exhibiting simple harmonic motion is conserved. SHM is a periodic motion.
What are the characteristics of oscillation?
- One type of oscillation is a periodic oscillation.
- A periodic oscillation is one that repeats itself.
- Period is the time it takes to complete one oscillation.
- Frequency is the number of oscillations per time.
Why SHM is called simple?
A very common type of periodic motion is called simple harmonic motion (SHM). In simple harmonic motion, the acceleration of the system, and therefore the net force, is proportional to the displacement and acts in the opposite direction of the displacement.
What is period in SHM?
The maximum x-position (A) is called the amplitude of the motion. The block begins to oscillate in SHM between x = + A and x = − A , where A is the amplitude of the motion and T is the period of the oscillation. The period is the time for one oscillation.
Why is SHM important?
Whilst simple harmonic motion is a simplification, it is still a very good approximation. Simple harmonic motion is important in research to model oscillations for example in wind turbines and vibrations in car suspensions.
What is the frequency of SHM?
Simple harmonic motion is repetitive. The period T is the time it takes the object to complete one oscillation and return to the starting position. The frequency f = 1/T = ω/2π of the motion gives the number of complete oscillations per unit time. It is measured in units of Hertz, (1 Hz = 1/s).
How does mass affect frequency of oscillation?
Mass on a Spring A stiffer spring with a constant mass decreases the period of oscillation. Increasing the mass increases the period of oscillation. For example, a heavy car with springs in its suspension bounces more slowly when it hits a bump than a light car with identical springs.
Is acceleration constant in SHM?
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.
What is the period of motion?
The period of the object’s motion is defined as the time for the object to complete one full cycle. Being a time, the period is measured in units such as seconds, milliseconds, days or even years. The standard metric unit for period is the second. An object in periodic motion can have a long period or a short period.