Exercise \(\PageIndex{1}\): Hooke's law and simple harmonic motion
The spring can be stretched by click-dragging the blue ball as shown in the animation (position is given in meters and time is given in seconds). Once you have dragged the blue ball into position, click the "play" button to show the motion of the blue ball. Restart.
- Over what range of compression and stretching is Hooke's law valid?
- Find the elastic limit of the spring.
- Determine the spring constant of the spring.
- Determine the mass of the blue ball.
- Over what range of compression and stretching is the motion of the spring simple harmonic?
Exercise \(\PageIndex{2}\): A ball attached to a spring: position vs. time graph
A ball on an air track is attached to a compressed spring as shown in the animation (position is given in meters and time is given in seconds). Restart.
- Determine which graph properly shows the position of the ball as a function of time.
- Determine the frequency and period of the motion.
- Write down the equation for \(x(t)\).
- If the mass of the ball is \(2\text{ kg}\), what is the spring constant?
Exercise \(\PageIndex{3}\): A ball attached to a spring: velocity vs. time graph
A \(1\text{-kg}\) ball on an air track is attached to a compressed spring as shown in the animation (position is given in meters and time is given in seconds). Restart.
- Determine which graph properly shows the velocity of the ball in the x direction as a function of time.
- Write down the equation for \(v_{x}(t)\).
- What is the total mechanical energy of the system?
Exercise \(\PageIndex{4}\): A ball attached to a spring: simple harmonic motion
A ball on an air track is attached to a compressed spring as shown in the animations (position is given in meters and time is given in seconds). Restart. Each of the five graphs CORRECTLY shows a different property of the motion of the ball. Determine whether the red ball undergoes simple harmonic motion, and state which graph(s) tell you this.
Exercise \(\PageIndex{5}\): Determine the spring constant of the spring
A \(500\)-gram red ball on an air track is attached to a compressed spring (at \(x = 0\text{ m}\) the spring is unstretched) as shown in the animation (position is given in meters and time is given in seconds). Determine the spring constant of the spring (assume \(v = 0\text{ m/s}\) at the beginning and end of the animation). Restart.
Exercise \(\PageIndex{6}\): Determine several properties of the mass-spring system
A \(200\)-gram mass is vibrating at the end of a spring as shown (position is given in centimeters and time is given in seconds). Restart.
- What is the spring constant?
- What is the total mechanical energy of the system?
- What is the maximum velocity of the ball?
Exercise \(\PageIndex{7}\): Which graph properly denotes position versus time?
The animation shows the analogy between circular motion (coin on a turntable) and simple harmonic motion (hanging mass on a spring). Restart. Given the animation (position is given in meters and time is given in seconds), which graph properly denotes position vs. time for a horizontal spring synchronized with the turntable?
Exercise \(\PageIndex{8}\): What is the maximum speed of the hanging mass?
The animation shows the analogy between circular motion (coin on turntable) and simple harmonic motion (hanging mass on a spring). Given the above animation (position is given in meters and time is given in seconds), what is the maximum speed of the hanging mass? Restart.
Exercise \(\PageIndex{9}\): Which graph properly shows the position/velocity/acceleration?
A ball on a string oscillates as shown in the animation (position is given in meters and time is given in seconds). Restart.
- Determine which graph properly shows the position of the ball in the \(x\) direction as a function of time.
- Determine which graph properly shows the velocity of the ball in the \(x\) direction as a function of time.
- Determine which graph properly shows the acceleration of the ball in the \(x\) direction as a function of time.
Take data from the graph and answer the following:
- Write down the equation for \(x(t)\).
- Write down the equation for \(v(t)\).
- Write down the equation for \(a(t)\).
- Write down the equation for \(v(x)\).
Exercise \(\PageIndex{10}\): Determine the effective acceleration due to gravity
A pendulum is allowed to oscillate in an accelerating elevator as shown in the animation (position is given in meters and time is given in seconds). Determine the effective acceleration due to gravity by analyzing the motion. Restart.
Exercise \(\PageIndex{11}\): Dig a hole through the center of the Earth
A very wealthy individual proposes to dig a hole through the center of Earth and run a train (the small black circle) from one side of Earth to the other, as shown in the animation (position is given in Earth radii and time is given in seconds). Which of the animations correctly depicts the motion of the train? Ignore frictional effects and treat Earth as a uniform mass distribution. Restart.
Exercise \(\PageIndex{12}\): A block floating in water is displaced from equilibrium
Two identical cubes (\(l = 10\text{ cm}\)) are floating in water (\(\rho = 1000\text{ kg/m}^{3}\)). The one on the left is in equilibrium. The one on the right is initially displaced from equilibrium. Restart.
- What is the condition for equilibrium?
- For the oscillating cube, what is the net force acting on the cube?
- For the oscillating cube, what is the period of oscillation?
- Determine the mass of the cubes.
Physlets were developed at Davidson College and converted from Java to JavaScript using the SwingJS system developed at St. Olaf College.
