Scribd
Upload
38 views3 pages

Experiment No 2

The objective of the experiment is to study un-damped free vibrations of a mass spring system by determining the natural frequency and time period of oscillation. The apparatus consists of a simple mass spring system with weights and a stopwatch. Measurements of static deflection, time for 20 oscillations, and calculations of theoretical, experimental, and inspired natural frequencies and time periods will be recorded in a table. Precautions include ensuring only vertical vibration, avoiding large spring deflections, including hanger mass, and avoiding parallax error.

Uploaded by

abdul rehman
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
38 views3 pages

Experiment No 2

The objective of the experiment is to study un-damped free vibrations of a mass spring system by determining the natural frequency and time period of oscillation. The apparatus consists of a simple mass spring system with weights and a stopwatch. Measurements of static deflection, time for 20 oscillations, and calculations of theoretical, experimental, and inspired natural frequencies and time periods will be recorded in a table. Precautions include ensuring only vertical vibration, avoiding large spring deflections, including hanger mass, and avoiding parallax error.

Uploaded by

abdul rehman
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
You are on page 1/ 3

EXPERIMENT 2

OBJECTIVE:
To study un-damped free vibrations of a vertical spring mass system by determining the natural
frequency and time period of oscillation and comparing the experimental results with theoretical
expectations.

APPARATUS:

Simple Mass Spring System, weights, stopwatch

THEORY:
Helical or coil springs are commonly used in wide variety of
mechanical systems. Their basic work is to produce a force which is
proportional to the deflection or vice versa. Figure-1 shows a typical
force-deflection diagram for a helical spring. In the linear region of
this diagram, the relation between force and deflection obeys Hook's
Law: i.e. deformation varies linearly with the load applied within the
elastic limit.

∆F = 𝑘∆𝑥

Where k is called stiffness of the


spring (N/m). The reciprocal of k is
called deflection coefficient which is
the deflection introduced by a unit
force.

If a mass is attached to one end of a spring while the other end is fixed, the resulting system is called
simple mass-spring which oscillates harmonically according the following equation (neglecting all
types of damping forces):

Σ𝐹x = 𝑚𝑥
𝑚𝑔 − 𝐾(𝑠 + 𝑥) = 𝑚𝑥

At rest mg = 𝑘𝑠

So,

𝑚𝑥 = −𝐾𝑥  𝑚𝑥 + 𝐾𝑥 = 0
𝐾
𝑥+
𝑚
𝑥=0

Department of Technology
𝑘 𝑚
𝜔𝑛𝑡ℎ𝑒𝑜 = √ ; 𝜏𝑡ℎ𝑒𝑜 = 2𝜋 √
𝑚 𝑘

2𝜋
𝜔nexp. =
𝜏exp.

𝑔 𝛿𝑠𝑡
𝜔𝑛𝑖𝑛𝑠𝑝 = √ ; 𝜏𝑖𝑛𝑠𝑝 = 2𝜋 √
𝛿 𝑠𝑡 𝑔

For un-damped free vibrations


𝑥𝑜 𝑣𝑎𝑙𝑢𝑒𝑡ℎ𝑒𝑜 − 𝑣𝑎𝑙𝑒𝑒𝑥𝑝
𝑥 (𝑡) = 𝑥𝑜 cos 𝜔𝑛 t + sin 𝜔𝑛 t ; % 𝑒𝑟𝑟𝑜𝑟 = 𝑒 = × 100
𝜔𝑛 𝑡ℎ𝑒𝑜

PROCEDURE:

Part A; Static Deflection

1. Hang the spring with the hook of the frame.


2. Add weights in an incremental fashion and record the corresponding deflection.

Part B; Oscillatory Motion

1. Pull down the mass and release it to introduce oscillatory motion.


2. Add masses incrementally and measure the time of 20 oscillations.
3. Record your readings as shown in the following table.

OBSERVATIONS AND CALCULATIONS

Static Time Period 𝝎𝒏


Time for 20 %
Mass Deflection 𝝉𝑬𝒙𝒑 𝝉𝑰𝒏𝒔𝒑 𝝉𝑻𝒉𝒆𝒐. 𝝎𝒏𝒆𝒙𝒑. 𝝎𝒏𝒊𝒏𝒔𝒑. 𝝎𝒏𝒕𝒉𝒆𝒐.
(𝜹𝒔𝒕) oscillations error
(g)
(sec) (sec) (sec) (sec) (rad/s) (rad/s) (rad/s) in 𝝉
(mm)

PRECAUTIONS:

1. Make sure the system only vibrates in vertical plane.


2. Do not produce very large deflections/oscillations in spring.
3. Include the mass of the hanger in total mass.
4. Spring should not be deformed.
5. Avoid parallax error while measuring deflection

Department of Technology
Results and Discussion

Sample Calculation

Department of Technology

You might also like