A pendulum is a weight hung from a fixed point. Pendulums swing back and forth in a regular motion known as a period. The period of a pendulum is affected by the length of the string/rod. A spring is a resilient device that can be pressed or pulled but return to its original shape when released.

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## How is pendulum similar to spring?

The pendulum has a restorative force and oscillating pattern similar to that of a spring. A swinging pendulum passes through the resting position and continues to swing until it reaches a certain distance past the equilibrium.

## Does Hooke’s law apply to pendulum?

The motion of a simple pendulum is very close to Simple Harmonic Motion (SHM). SHM results whenever a restoring force is proportional to the displacement, a relationship often known as Hooke’s Law when applied to springs. Where F is the restoring force, k is the spring constant, and x is the displacement.

## What are the differences between mass spring system and simple pendulum?

The period of oscillation of a simple pendulum does not depend on the mass of the bob. By contrast, the period of a mass-spring system does depend on mass. Explain this apparent contradiction. The reason the simple pendulum has no dependence on mass is because the mass gets to “count” for two different things.

## What is the formula for spring pendulum?

K=mโ22(หz2+(z+1)2หฮธ2),ฮ =k2(โz+mgk)2+mgโ[1โ(z+1)cosฮธ].

## Is a spring a simple pendulum?

In physics and mathematics, in the area of dynamical systems, an elastic pendulum (also called spring pendulum or swinging spring) is a physical system where a piece of mass is connected to a spring so that the resulting motion contains elements of both a simple pendulum and a one-dimensional spring-mass system.

## What does the period of a pendulum depend on?

So, to recap, the period of a pendulum depends on the length of the pendulum and the surface gravity of the planet that you’re on. It does not depend on the amplitude or the mass of the pendulum.

## Why is simple pendulum simple harmonic motion?

For small displacements of less than 15 degrees, a pendulum experiences simple harmonic oscillation, meaning that its restoring force is directly proportional to its displacement. A pendulum in simple harmonic motion is called a simple pendulum.

## How many degrees of freedom does a spring pendulum have?

The motion of the two degrees of freedom (DOF) spring pendulum with internal resonance in the presence of an excitation force directed along the arm of the spring is investigated in [4] while its chaotic responses are examined in [5].

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

The period of a spring-mass system is proportional to the square root of the mass and inversely proportional to the square root of the spring constant.

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

For equal displacements, the applied force and the restoring force are equal and opposite. 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.

## Why simple pendulum is called simple?

The simple pendulum (see wikipedia or hyperphysics) leads to a simple differential equation by using Newton’s second law: ยจฮธ+glsin(ฮธ)=0. This pendulum gives the easiest way te look at harmonic motion. The above case is what they call the simple pendulum.

## What is K for a pendulum?

K is the spring constant. The pendulum is a simple harmonic oscillator with spring constant, K.

## Why does the mass of a pendulum not affect the period?

Answer and Explanation: The mass of a pendulum doesn’t affect the period because the force that acts on the pendulum is gravity. The force and the mass are proportional, so if the pendulum has more mass, it will feel more force.

## How do you know if a spring is in series or parallel?

Note: When two or more springs are connected end-to-end or point-to-point in mechanics, they are said to be in series, and when they are connected side-by-side, they are said to be in parallel; in both cases, they act as a single spring.

## What are mass spring systems used for?

What is Spring Mass System? A spring-mass system in simple terms can be described as a spring sytem where a block is hung or attached at the free end of the spring. The spring-mass system can usually be used to find the period of any object performing the simple harmonic motion.

## What is the spring equation?

The equation for determining the force a spring exerts is Fs=โkฮx F s = โ k ฮ x where k is an experimentally determined figure called the spring constant which reports the amount of force exerted by the spring per meter of stretch or compression and ฮx is the distance the spring is stretched or compressed from its …

## What is the constant of a spring?

The spring constant is the force needed to stretch or compress a spring, divided by the distance that the spring gets longer or shorter.

## What is the formula for length of simple pendulum?

For simple pendulum of length L is equal to the radius of the earth ‘R’, L = R = 6.4 x 106 m, then the time period T = 2ฯ โR/2g.

## How do you find the period of oscillation of a spring?

Mass on a spring – Where a mass m attached to a spring with spring constant k, will oscillate with a period (T). Described by: T = 2ฯโ(m/k). By timing the duration of one complete oscillation we can determine the period and hence the frequency.

## How does spring constant affect period?

Bigger mass means you would get more period because there’s more inertia, and it’s also affected by the spring constant. Bigger spring constant means you’d have less period because the force from the spring would be larger.

## How do you find the amplitude of oscillation of a spring?

It moves through the equilibrium position of the vertical spring with its maximum velocity vmax = 1.5 m/s. Its velocity as a function of time is v(t) = -ฯAsin(ฯt + ฯ). Details of the calculation: Since vmax = ฯA and ฯ = 2/s, the amplitude of the amplitude of the oscillations is A = 0.75 m.

## Why does a shorter pendulum swing faster?

A pendulum with a longer string has a lower frequency, meaning it swings back and forth less times in a given amount of time than a pendulum with a shorter string length.

## Why does increasing the length of a pendulum affect its period?

A pendulum with a longer length takes longer to cover the distance to swing from one side to the other. Since the period of a pendulum is the amount of time it takes for the weight to swing and then return to its original position, this will mean a longer period.

## Which pendulum will swing faster?

Shorter pendulums swing faster than longer ones do, so the pendulum on the left swings faster than the pendulum on the right. pendulums to one side, and then let them swing. Notice that, if you start them swinging at the same time, they return to their starting points at the same time.