Simple Harmonic Motion - Lab report PDF

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Physics Lab report
Title - Simple Harmonic Motion...

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Title of the lab : Simple Harmonic Motion Purpose of the lab The purpose of this lab was to observe the oscillatory motion and determine how variables like stretch of spring, spring constant, mass, length, and angle of oscillation affect the period of the motion. Physical laws/formulas Hooke's Law states that the force needed to compress or extend a spring is directly proportional to the distance you stretch it. F = - k.x

where k = spring constant and x = stretch of the spring

Period of mass - spring system T= 2pi√(m/k) Period of simple pendulum T= 2pi√(L/g)

where L = length of the string

Body of the lab report A. Mass on a spring 1-2 . Calculating Kweak , Kmedium ,and Kstrong

Kweak = 6.28 N/m

Kmedium = 15.4 N/m

Kstrong = 71.8 N/m

3. Test dependence of T on m, x, and K Time t for 10 oscillations, T=t/10 a. Changing x ( Kmedium and m fixed) x(m)

T(seconds)

0.01

0.416

0.02

0.427

0.03

0.421

0.04

0.419

Here, we see that the period of oscillation remains constant even when we increase the stretch of the spring. Hence, the spring stretch doesn’t affect the period of motion.

b. Changing m ( Kmedium and x fixed)

m(kg)

T(seconds)

0.02

0.422

0.04

0.473

0.06

0.540

0.08

0.560

Increasing the mass increases the period of oscillation. Hence, the period of oscillation is directly proportional to the mass on spring.

c. Changing K(x and m fixed) K

T(seconds) 0.934

Kweak 0.562 Kmedium 0.284 Kstrong

The period of oscillation is inversely proportional to the spring constant. A stiffer spring with a constant mass decreases the period of oscillation.

Overall, we can say that the period of oscillation of mass on a spring depends upon the spring constant and the mass while it is independent of the stretch of the spring.

B. Mass on pendulum a.Changing θ ( L and m fixed)

θ(degrees)

T(seconds)

10°

1.145

20°

1.170

30°

1.161

40°

1.180

The starting angle of the pendulum, as we see, doesn’t affect the period of the pendulum because it takes the same time for the pendulum to return back to the position where it started.

b.Changing m ( L and θ fixed) m(kg)

T(seconds)

0.05

1.160

0.1

1.170

0.15

1.170

0.2

1.188

The period of oscillation remains constant when the mass is increased. Hence, mass doesn’t affect the period of motion.

c. Changing L ( m and θ fixed) L(m)

T(seconds)

0.32

1.130

0.28

1.09

0.24

1.007

0.18

0.92

The longer the length of string, the farther the pendulum falls and therefore, the longer the period. Hence, decreasing the length of the string decreases the time period and increasing the length of the string increases the period of motion. Therefore, the period of motion of a pendulum depends upon the length of string, and amplitude(angle) but is independent of the mass. CONCLUSION Therefore, we can conclude that the period of motion of spring depends upon the spring constant and mass while the period of motion of pendulum depends upon the length of the string....