Question

Question )

a) Briefly state an explanation of what the helical spring in simple harmonic motion and its concepts are in min 300 words? (In word text, no pictures)

b) What is the Aim of The helical spring in simple harmonic motion experiment where in oscillations of 30 how long it takes or the time it takes for each set of weights is measured?(min 100 words)

Answer 1

The suspension system in modern cars and bikes lets the wheels move up and down to absorb small bumps while keeping the tyres in contact with the ground for better control. Additionally the suspension prevents the full effect of the bumps being transferred to the rider or passengers.

Many different techniques are used in modern suspension systems but each must have some form of 'springiness'. A simple helical spring is frequently used in the simplest suspension systems. These springs are compressed by the movement of the vehicle over bumpy ground in such a way that distance moved by the passengers is less than that moved by the wheel.

Advances in engineering have taken the design of modern suspension systems well beyond the scope of this chapter, nevertheless their behaviour depends on understanding the basics of a system in which a mass oscillates on the end of a spring.

This section looks at the behaviour of a spring when masses are added to it. The forces in the spring are tension forces rather then compression forces.They are made of wire coiled into a helical form, the load being applied along the axis of the helix. In these type of springs the major stresses is torsional shear stress due to twisting. They are both used in tension and compression.

The major stresses in a helical spring are of two types, shear stress due to torsion and direct shear due to applied load.

Advantages Of Helical Springs:

* Easy to mfg.
* Available in wide range.
* Reliable.
* Constant spring constant.
* Performance is accurate.
* Characteristics can be varied by changing dimensions.

Applications Of Springs:

* Absorbs energy due to shock or vibration.
* To apply force in brake, clutches, spring loaded values.
*To measure forces in spring balance and engine indicators.

*To store energy.

Material of Helical Spring:

* High Fatigue Strength

* High Ductility

* High Resistance

Part(B)

Consider a mass m suspended at rest from a spiral spring and let the extension produced be e. If the spring constant is k we have:

mg = ke

The mass is then pulled down a small distance x and released. The mass will oscillate due to both the effect of the gravitational attraction (mg) and the varying force in the spring (k(e + x)).

At any point distance x from the midpoint:

restoring force = k(e + x) - mg

But F = ma, so ma = - kx and this shows that the acceleration is directly proportional to the displacement, the equation for s.h.m.
The negative sign shows that the acceleration acts in the opposite direction to increasing x.

From the defining equation for s.h.m. (a = -w2 x) we have w = k/m = g/e
and therefore the period of the motion T is given by:

Period of oscillation of a helical spring (T ) = 2p(m/k)1/2 = 2p(e/g)1/2.

If the mass of the spring is significant we can allow for it and the corrected equation becomes:

Spring of mass 3M (T) = 2p(m+M/k)1/2

where M is one-third of the mass of the spring. The mass must be sufficiently large to keep the coils opened.