What do a spring and a pendulum have in common?

Both Spring and Pendulum motion is PERIODIC. They undergo SIMPLE HARMONIC MOTION.

How are Hooke’s law and simple harmonic motion related?

In simple harmonic motion the period and frequency are independent of the amplitudes of the oscillations. Therefore, Hooke’s Law provides the conditions for simple harmonic motion and the spring constant can be used with Equation (2) to measure the period of a mass vibrating on a spring.

Is a pendulum in simple harmonic motion?

For small displacements, a pendulum is a simple harmonic oscillator. A simple pendulum is defined to have an object that has a small mass, also known as the pendulum bob, which is suspended from a light wire or string, such as shown in Figure 1.

What is spring harmonic motion?

Simple harmonic motion is typified by the motion of a mass on a spring when it is subject to the linear elastic restoring force given by Hooke’s Law. A system that follows simple harmonic motion is known as a simple harmonic oscillator.

What is the equilibrium position of a pendulum?

When the pendulum is at rest, not swinging, it hangs straight down. This position is called the “equilibrium position.” It is convenient to take this position as the reference position mentioned as the “origin” in the definition of position.

What is a returning force called?

In physics, the restoring force is a force which acts to bring a body to its equilibrium position. The restoring force is often referred to in simple harmonic motion. The force which is responsible to restore original size and shape is called restoring force.

What is K in F KX?

The proportional constant k is called the spring constant. It is a measure of the spring’s stiffness. When a spring is stretched or compressed, so that its length changes by an amount x from its equilibrium length, then it exerts a force F = -kx in a direction towards its equilibrium position.

What is the relationship between mass and period of a pendulum?

The period of a pendulum does not depend on the mass of the ball, but only on the length of the string. Two pendula with different masses but the same length will have the same period. Two pendula with different lengths will different periods; the pendulum with the longer string will have the longer period.

Why are pendulums not SHM?

Any pendulum undergoes simple harmonic motion when the amplitude of oscillation is small. The pendulum still oscillates, but the motion is no longer simple harmonic motion because the angular acceleration is not proportional to the negative of the angular displacement.

Why do shorter pendulums swing faster?

Why does the angle the pendulum starts at not affect the period? (Answer: Because pendulums that start at a bigger angle have longer to speed up, so they travel faster than pendulums that start at a small angle.)

What is the full form of SHM?

Simple harmonic motion is defined as a periodic motion of a point along a straight line, such that its acceleration is always towards a fixed point in that line and is proportional to its distance from that point.

WHAT IS A in SHM?

Each of these constants carries a physical meaning of the motion: A is the amplitude (maximum displacement from the equilibrium position), ω = 2πf is the angular frequency, and φ is the initial phase.

How does Hooke’s law relate to simple harmonic motion?

Because the force is proportional to displacement of the spring from its equilibrium position, a mass attached to the spring will undergo simple harmonic motion. In this lab we will verify Hooke’s Law and learn about simple harmonic motion. The motion of the spring will be compared to motion of a pendulum.

How to test your understanding of Hooke’s law?

Test your understanding with practice problems and step-by-step solutions. Browse through all study tools. You have a lightweight spring whose unstretched length is 6.25 cm. First, you attached one end of the spring to the ceiling and hang a 4.7 gram mass from it. This stretches the spring to a length o…

How does Hooke’s law apply to a hanging mass?

For a mass hanging from a spring, Hooke’s law states that the force, F, applied to the hanging mass is proportional to the displacement, (x-x 0 F =−k⋅ (x -x 0 ) ), of the mass from its equilibrium position without the mass, that is, , where k is the spring constant.

How is the force of an ideal spring governed by Hooke’s law?

Introduction The force applied by an ideal spring is governed by Hooke’s Law : F = -kx. Because the force is proportional to displacement of the spring from its equilibrium position, a mass attached to the spring will undergo simple harmonic motion. In this lab we will verify Hooke’s Law and learn about simple harmonic motion.