SKH St. Mary S Church Mok Hing Yiu College

SKH St. Mary’s Church Mok Hing Yiu College Physics Experiment Form 6S

Student Name : ______( ) Date : ______Group Number : ______Marks : ______E5 The Oscillation of a Mass-Spring System

Objectives : * To investigate how the period of oscillation of a mass hanging from a spring varies with the mass. * To measure the force constant spring.

Apparatus : Light spring 1 Slotted weight with hanger 10 × 20 g Retort stand and clamp 1 Stop watch 1 Metre rule 1 Theory : For a spring, the force exerted F is proportional to the displacement x the spring is compressed or stretched, and the proportionality constant is called k, known as the force constant. This is known as Hooke’s Law, F = -kx For a body of mass m attached to the spring, the acceleration of the body a will be given by Newton’s second law, F = ma and thus combining the two equations gives k a   x m Since a  x , then we have satisfied the condition for SHM, and in this case the angular frequency  is given by k   m m which gives T  2 k

Procedure : (A) Hooke’s Law Retort stand

1. Hand the spring from a retort stand and clamp Metre rule so that is has room to stretch. 2. Use a metre rule to measure the position of the bottom of the spring. Choose a point that can Clamp be found easily over and over. Spring 3. Gently hand a slotted weight of mass 20 g on the bottom of the spring. Measure and record the new position of the bottom of the spring. 4. Repeat, adding 20 g each time, noting the position Slotted weight of the bottom of the spring.

E5 The Oscillation of a Mass-spring System - 1 (B) Simple Harmonic Motion 5. Using a retort stand and clamp, suspend the spring with a slotted weight hanger of mass 20 g vertically so that it can move freely up and down as shown below. Clamp

Spring

Retort stand

Slotted weight

6. Displace the hanger a bit downward and then release it, it should oscillate vertically about its rest position. 7. Measure the time taken for the 20 complete oscillations with a stop watch. Calculate the period T of the hanger. 8. Repeat the timing once for different amplitude. Compare the periods for the different amplitudes. The period should not depend on the amplitude of the oscillation. 9. Repeat the experiment several times using different masses suspended at the end of the spring. Tabulate the results in the table shown below. Results : (A) Hook’s Law

Mass hanging on spring /kg 0 Position of spring /cm Extension of spring /m

Plot a graph of the mass hanging on the spring against the extension of the spring.

From the above graph, find the force constant of the spring in N m-1.

E5 The Oscillation of a Mass-spring System - 2 ______

(B) Simple Harmonic Motion

Time for 20 oscillations /s Mass on Mean period of spring /kg Amplitude = cm Amplitude = cm oscillation T /s t1 /s T1 /s t2 /s T2 /s

Plot a suitable graph to show how the period of oscillation varies with the mass hanging on the spring.

(i) From the graph, find the force constant of the spring, ______

E5 The Oscillation of a Mass-spring System - 3 ______(ii) Compare the answer to (i) with that obtained from part (A). Account for any discrepancy. ______Questions : 1. State the main precautions in performing this experiment. ______2. Discuss the main sources of error in this experiment. ______

3. Practically the oscillating ‘mass’ mo includes a portion of mass called the effective mass of the spring that can be imagined on the end of an ideal, massless spring; theoretical consideration of the kinetic energy of the vibrating spring gives this amount as 1/3 the actual mass of the spring. The graph you have drawn in part (B) may not pass through the origin. (i) Derive an expression to show that the intercept on the m-axis gives the effective mass of the spring. ______(ii) Hence find the value of the effective mass of the spring from your graph. ______

E5 The Oscillation of a Mass-spring System - 4