Find g using oscillations of a mass-spring system.

Experiment to determine acceleration due to gravity using a mass-spring system by measuring oscillation time, extension, and applying SHM relations.

Apparatus

The experiment requires a helical spring of known spring constant (K), an iron stand with a clamp, slotted weights, and a stopwatch for timing oscillations. All equipment should be properly aligned before beginning the procedure.

Observations and Calculations

No.of abs	Oscillating mass ‘M’ gms	Time for 10 vibrations			Time period T=t/20	Extension Produced Weights in gms ‘a’ cm
		1 sec	2 sec	Mean ‘t’ sec
1 2 3	20 40 60				20 20 20

Mean value of ‘g’=………………………cm/s

Procedure

First, suspend the helical spring from the clamp of the iron stand and attach a hanger to its lower end.
Load the hanger with different weights and observe the corresponding extension on the attached scale.
Next, slightly pull the hanger downward to start the oscillation and record the time for 20 vibrations.
Repeat this measurement twice and take the mean value of the time.
Therefore, calculate the acceleration due to gravity (g) using the formula:

g = 4π² (a / T²)
Perform the same steps for different weights to get several readings.
Finally, compute the mean value of g from all observations to ensure accuracy.

Formula Used

$\frac{a}{T²}$

Where:

g = acceleration due to gravity
a = extension produced
T = time period of oscillation

Inference

The experiment verifies that the acceleration due to gravity can be determined using a mass-spring system performing simple harmonic motion. The calculated values of g remain nearly constant for all readings, confirming the accuracy of Hooke’s Law and SHM principles.

Precautions

Make sure the spring is elastic and free from kinks.
The table and stand must remain stable during oscillations.
Start the stopwatch precisely when the oscillation begins.
Avoid overloading the spring to stay within the elastic limit.
Repeat readings to minimize human and mechanical errors.

Viva Voce

Q1. What is meant by restoring force?
A: The restoring force brings a vibrating system back toward its mean position.

Q2. What are the factors responsible for oscillatory motion?
A: The main factors are restoring force and inertia.

Q3. What is Simple Harmonic Motion (SHM)?
A: It is the motion in which acceleration is directly proportional to displacement and always directed toward the mean position.

Q4. What is the spring constant?
A: The ratio of the applied force to the extension produced in the spring, i.e., k = F/x.

Q5. Define elastic limit.
A: The maximum limit of stress after which a material stops obeying Hooke’s Law.

Q6. State Hooke’s Law.
A: Within the elastic limit, the force applied to a spring is directly proportional to its extension.

Q7. What is a helical spring?
A: A spring coiled in the shape of a helix is called a helical spring.

Q8. What type of energy is stored in a stretched spring?
A: Elastic potential energy.

Q9. Define stress and strain.
A:

Stress: Force per unit area acting on a body.
Strain: Ratio of change in length to the original length.

Q10. What are the characteristics of SHM?
A:

Acceleration ∝ displacement from the mean position.
It is always directed toward the mean position.
Total energy remains constant during motion.

Q11. How is “g” calculated using a mass-spring system?
A: Measure the extension (x) and time period (T) of oscillation, then apply the formula: