AP Physics 1 - Pendulums

In the lab, a student has created a pendulum by hanging a weight from a string. The student releases the pendulum from rest and uses a sensor and computer to find the equation of motion for the pendulum: $x(t)=0.13m;cos(6.3\frac{radians}{s}t+0.14:radians)$

The student then replaces the weight with a weight whose mass, is twice as large as that of the original weight without changing the length of the string. The student again releases the weight from rest from the same displacement from equilibrium. What would the new equation of motion be for the pendulum?

Which simple pendulum will have a longer period?

$A:m = 10\textup{ kg}, L = 2\textup{ m}$

$B: m = 4\textup{ kg}, L = 3\textup{ m}$

$g = 10\ \frac{\textup{m}}{\textup{s}^2}$

A pendulum has a period of 5 seconds. If the length of the string of the pendulum is quadrupled, what is the new period of the pendulum?

$g=10\frac{m}{s^2}$

A simple pendulum with a length of $L = 2\textup{ m}$ has a block of mass $m = 6\textup{ kg}$ attached to the end. If the pendulum is $h=1\textup{ m}$ above its lowest point and rotating downward, what is the instantaneous acceleration of the block?

$g = 10\ \frac{\textup{m}}{\textup{s}^2}$

A simple pendulum of length $L = 4\textup{ m}$ has a block of mass $m = 10\textup{ kg}$ attached to the end of it. The pendulum is originally at an angle of $\theta = 5^{\circ}$ to the vertical and at rest. If the pendulum is released and allowed to rotate freely at time , what is the angle of the pendulum at time $t = 10\textup{ s}$ ?

$g = 10\ \frac{\textup{m}}{\textup{s}^2}$

A simple pendulum has a length $L = 1.4\textup{ m}$ has a block of mass $m = 6\textup{ kg}$ attached to one end. If the pendulum is released from rest, what is the maximum centripetal acceleration felt by the block?

$g = 10\ \frac{\textup{m}}{\textup{s}^2}$

A pendulum of length has a mass of attached to the bottom. Determine the frequency of the pendulum if it is released from a shallow angle.

Consider the following system:

Pendulum_1

If the length of the pendulum is and the maximum velocity of the block is $3\frac{m}{s}$ , what is the minimum possible value of angle A?

$g = 10\frac{m}{s^2}$

A student studying Newtonian mechanics in the 19th century was skeptical of some of Newton's concepts. The student has a pendulum that has a period of 3 seconds while sitting on his desk. He attaches the pendulum to a ballon and drops it off the roof of a university building, which is 20m tall. Another student realizes that the pendulum strikes the ground with a velocity of $12\frac{m}{s}$ . What is the period of the pendulum as it is falling to the ground?

Neglect air resistance and assume $g=10\frac{m}{s^2}$

Matt Damon is once again trapped on Mars. He must measure the length of rope he has using only a stopwatch. Please solve the problem below.

A pendulum on Mars has been measured to have a period of seconds. Using the knowledge that gravity on Mars is $3.711\frac{m}{s^2}$ determine the length of the simple pendulum. Round to 3 significant figures.

Pendulums

Practice Questions