1. OBJECTIVE Experiment 3: Mechanical Behavior of a Spring 2. THEORY To understand mechanical behaviour of a spring by using Hooke's law and simple harmonic motion and to determine the value

of spring constant of a spring by static and dynamic methods [¹] A spring is an elastic object which stores mechanical energy. Springs are usually made of hardened steel. Small springs can be wound from pre-hardened steel, while larger ones are made from annealed steel and hardened after fabrication. Some non-ferrous metals, such as phosphor bronze and titanium, are also used in making spring. The spring constant, k, of an ideal spring is defined as the force per unit length and is different from one spring to another. Spring constant is represented in Newton/meter (N/m). It can be determined both in static (motionless) as well as dynamic (in motion) conditions. Two different techniques are used for determination of the spring constant. In the static method, Newton's second Law is used for the equilibrium case, and laws of periodic motion are applied for determining the spring constant in the dynamic case. Static mode In this mode of determination of spring constant, a weight is added to the spring and its extension is measured. The spring is fixed at one end and a weight is added in equal amounts one by one. The extension produced in the length of the spring is noted from the meter scale fixed. After adding a weight the spring will attain a stationary position after some time. At equilibrium, there are two equal and opposite forces, acting upward and downward. In the static mode the spring constant obtained by this method is denoted by ks; the subscript "s" indicates that the static method has been employed for determination of the spring constant. In the equilibrium condition, Upward force, Fup= Downward force, Fdown Where Fup = kse Fdown = mg Equating the RHS of the above two equations kse = mg mg ks m is the mass of the load applied (kg) g is the acceleration due to gravity (9.81 m/s²) e is the extension of the massless spring (mm) k, is the spring constant in the static condition. (N/mm)/nDynamic mode If the spring is made to oscillate by pulling the weight applied to it downward, it executes a simple harmonic motion; the equation representing its motion is written as The angular velocity is given by: d²y_ky dxz = Therefore, the time period of the oscillation of the spring is: Where T = 2π Rearranging the equation to find the spring constant in dynamic method, 4n²m 10007² m i. ka m is the mass of the load applied (kg) k is the spring constant in the dynamic condition. (N/mm) T is the time period of oscillation (s) [1] ttp://kamaljeeth.net/newsite/index.php?route=product/product/getProductAttachmentFile&attachment_id=301 3. PROCEDURE a) Static Method: Record the mass of the load. ii. Measure the nominal length (original length) of the spring. iii. Apply the mass on the end of the spring and measure the extended length. Repeat step 3 two more times and take the average extension. iv. V. Using the hooke's law equation, calculate the static spring constant for the spring. vi. Repeat the procedure for different masses./nالـكـلـيـة الأسـتـرالـيـة فـي الـكـويت Australian College of Kuwait i. ii. iii. iv. V. V. b) Dynamic Method: Record the mass of the load. Apply the mass on the end of the spring until it reaches equilibrium. Extend the spring by a certain amount and release the spring to make it oscillate. Note the time taken for "N" number of oscillations. Repeat step 4 three more times and take the average time taken for 15 oscillations. Using the simple harmonic motion equation, calculate the dynamic spring constant for the spring. vi. Repeat the procedure for different masses and different springs 4. DATA AND RESULTS a) Static Method Table 1b. Spring 1 Initial Length: Lab Worksheet Guidelines Mass in kg Force in N Trial 1 Trial 1 b) Dynamic Method Table 2a. Spring 1 N (number of oscillations): Mass in kg Extension in mm Trial 2 Time for N oscillations in secs Trial 2 Trial 3 Trial 3 Average Average Period T in secs T² in secs² Spring Constant k, in N/mm Spring Constant ka in N/mm