Question

A pendulum, with 1 kg mass attached with string of length 1 m is raised to an angle of 30 degrees below the horizontal and then released. Neglect frictional forces.

1. What is the height, h, initially of the pendulum bob?

2. What is the Potential Energy initially? What is the total Energy of the system?

3. What is the velocity of the pendulum when it reaches the bottom of its swing (i.e at 90° from horizontal as also shown above)? 4. If the period is given as T = 2.15s, what is the frequency?

5. Plot the motion of the pendulum as a wave (2 plots – position vs. time and velocity vs. time). Make sure to label correctly with correct values (x axis (time at correct values), y axis, amplitude, frequency, wavelength). Do NOT Forget to find and Label wavelength.

6. What type of wave is this?

Answer 1

Q1. initial height h=length of the string*(1-sin(angle))=1*(1-sin(30))=0.5 m

Q2.

initial potential energy=mass*g*h=1*9.8*0.5=4.9 J

as initially the bob is t rest, total mechanical energy of the system=4.9 J (as kinetic energy is 0)

Q3.

at the bottom of the swing, all the potnetial energy gets converted to kinetic energy

if speed is v m/s,

then 0.5*mass*v^2=m*g*h

==>v=sqrt(2*g*h)=sqrt(2*9.8*0.5)=3.1305 m/s

part 4:

frequency=1/period=0.46512 Hz

part 5:

angle theta at any time t is given by

theta=(pi/6)*cos(2*pi*t/T) radians

=(pi/6)*cos(2.9224*t) radians

then angular velocity=d(theta)/dt=-1.5302*sin(2.9224*t) rad/s

Q6.

it is a simple harmonic motion.