# Simple Harmonic Motion of a mass-spring system.

Immanuel Lutheran College

S.6 Physics (AL) 2003-2004

Experiment Report 1

Name:  Lam Kong Lan             Class:  6B              Class No.:  7

Title:  Simple Harmonic Motion of a mass-spring system

Objective:

1. To investigate the motion of a spring-mass system undergoing oscillation and to verify the relationship between the period of oscillation of a mass hanging from a spring and the mass.
2. To find out the force constant and effective mass of the spring.

Apparatus:

• Light spring
• Stop-watch
• Horizontal bar
• Balance
• Retort stand and clamp
• Slotted mass with hanger 2 ×100g and 5 × 20g

Theory:

By Hooke’s Law, for a mass m hanging from a spring, at the equilibrium position, the extension e of the spring is given by mg = ke where k is the force constant of the spring.

Let x be the displacement of spring from the equilibrium position, then we have an expression of the net force acting on the mass as  Fnet = -k( e + x ) + mg = -kx .

Here, the negative sign means that it is a restoring force and the direction of Fnet is always opposite to x.

Moreover, according to Newton’s second law, the equation of motion: Fnet = ma

∴  Fnet = ma = -kx,    then  a = - (k/m)x = -w2x

∴   =

As the mass m executes simple harmonic motion (SHM),

the period of oscillation is defined as

∴  T2 = 4π2()

Therefore, a graph with T2 as the y-axis and m as the x-axis has a slope of  which should be a straight line passing through the origin.

However, as the mass of the spring will affect T.  T should be equal to  where me is the effective mass of the spring.

From the graph, we can obtain the value of force constant k as k = Nm-1 and the effective mass of the spring as it is the intercept on the m-axis.

Procedure:

A. Setting up the mass-spring system

1. The light spring was hung from the horizontal bar.  The horizontal bar was then firmly clamped on a retort stand.
2. The 20g slotted mass was suspended at the other end of the spring.
3. After ...