## Intro to Simple Harmonic Motion

## Example

A mass-spring system with an angular frequency ω = 8π rad/s oscillates back and forth. (a) Assuming it starts from rest, how much time passes before the mass has a speed of 0 again? (b) How many full cycles does the system complete in 60s?

## Equations of Simple Harmonic Motion

A 4-kg mass on a spring is released 5 m away from equilibrium position and takes 1.5 s to reach its equilibrium position. (a) Find the spring’s force constant. (b) Find the object’s max speed.

## Example

What is the equation for the position of a mass moving on the end of a spring which is stretched 8.8cm from equilibrium and then released from rest, and whose period is 0.66s? What will be the object’s position after 1.4s?

## Example

- A small block is attached to an ideal spring and is moving in SHM on a horizontal, frictionless surface. When ...
- An object is undergoing SHM with period 0.900 s and amplitude 0.320 m. At t = 0 the object is at x = 0.320 m a...
- (a) Music. When a person sings, his or her vocal cords vibrate in a repetitive pattern that has the same frequ...
- A 0.500-kg mass on a spring has velocity as a function of time given by vx(t) = -(3.60 cm/s) sin[(4.71 rad/s)t...
- A 0.500-kg mass on a spring has velocity as a function of time given by vx(t) = -(3.60 cm/s) sin[(4.71 rad/s)t...
- A 0.400-kg object undergoing SHM has ax = -1.80 m/s^2 when x = 0.300 m. What is the time for one oscillation?
- Weighing Astronauts. This procedure has been used to “weigh” astronauts in space: A 42.5-kg chair is attached ...
- A small block is attached to an ideal spring and is moving in SHM on a horizontal, frictionless surface. When ...
- The point of the needle of a sewing machine moves in SHM along the x-axis with a frequency of 2.5 Hz. At t = 0...
- A 2.00-kg, frictionless block is attached to an ideal spring with force constant 300 N/m. At t = 0 the spring ...
- In a physics lab, you attach a 0.200-kg air-track glider to the end of an ideal spring of negligible mass and ...
- A 2.40-kg ball is attached to an unknown spring and allowed to oscillate. Figure E14.7 shows a graph of the b...
- A 2.40-kg ball is attached to an unknown spring and allowed to oscillate. Figure E14.7 shows a graph of the b...
- The wings of the blue-throated hummingbird (Lampornis clemenciae), which inhabits Mexico and the southwestern ...
- A machine part is undergoing SHM with a frequency of 4.00 Hz and amplitude 1.80 cm. How long does it take the ...
- The displacement of an oscillating object as a function of time is shown in Fig. E14.4 . What is (a) the frequ...
- The displacement of an oscillating object as a function of time is shown in Fig. E14.4 . What is (a) the frequ...