17. Periodic Motion

Intro to Simple Harmonic Motion (Horizontal Springs)

17. Periodic Motion

# Intro to Simple Harmonic Motion (Horizontal Springs) - Video Tutorials & Practice Problems

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concept

## Intro to Simple Harmonic Motion

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## Example

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Problem

ProblemA 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?

A

1/4 s; 480 cycles

B

1/8 s; 480 cycles

C

1/8 s; 240 cycles

D

1/4 s; 240 cycles

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concept

## Equations of Simple Harmonic Motion

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Problem

ProblemA 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.

A

3.28 N/m; 4.52 m/s

B

4.39 N/m; 5.25 m/s

C

17.54 N/m; 10.47 m/s

D

2.01 N/m; 3.54 m/s

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## Example

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Problem

ProblemWhat 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?

A

.88cos(19.04t); .79 m

B

.088cos(19.04t); .08 m

C

.88cos(9.52t); .86 m

D

.088cos(9.52t); .064 m

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## Example

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PRACTICE PROBLEMS AND ACTIVITIES (46)

- 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...
- (II) Consider two objects, A and B, both undergoing SHM, but with different frequencies, as described by the e...
- Astronauts in space cannot weigh themselves by standing on a bathroom scale. Instead, they determine their mas...
- A 100 g block attached to a spring with spring constant 2.5 N/m oscillates horizontally on a frictionless tabl...
- It has recently become possible to 'weigh' DNA molecules by measuring the influence of their mass on a nano-os...
- A mass hanging from a spring oscillates with a period of 0.35 s. Suppose the mass and spring are swung in a ho...
- A 1.0 kg block is attached to a spring with spring constant 16 N/m. While the block is sitting at rest, a stud...
- The position of a 50 g oscillating mass is given by 𝓍(t) = (2.0 cm) cos (10 t ─ π/4), where t is in s. Determ...
- The position of a 50 g oscillating mass is given by 𝓍(t) = (2.0 cm) cos (10 t ─ π/4), where t is in s. Determ...
- A 200 g mass attached to a horizontal spring oscillates at a frequency of 2.0 Hz. At t = 0 s, the mass is at x...
- A 200 g mass attached to a horizontal spring oscillates at a frequency of 2.0 Hz. At t = 0 s, the mass is at x...
- A block attached to a spring with unknown spring constant oscillates with a period of 2.0 s. What is the perio...
- A 1.00 kg block is attached to a horizontal spring with spring constant 2500 N/m. The block is at rest on a fr...
- A block attached to a spring with unknown spring constant oscillates with a period of 2.0 s. What is the perio...
- A 200 g air-track glider is attached to a spring. The glider is pushed in 10 cm and released. A student with a...
- An air-track glider attached to a spring oscillates with a period of 1.5 s. At t = 0 s the glider is 5.00 cm l...
- A 500 g wood block on a frictionless table is attached to a horizontal spring. A 50 g dart is shot into the fa...
- An air-track glider is attached to a spring. The glider is pulled to the right and released from rest at t = 0...
- A 200 g mass attached to a horizontal spring oscillates at a frequency of 2.0 Hz. At t = 0 s, the mass is at x...
- (II) A small fly of mass 0.28 g is caught in a spider’s web. The web oscillates predominantly with a frequency...
- (II) A tuning fork oscillates at a frequency of 441 Hz and the tip of each prong moves 1.8 mm to either side o...
- (II) A tuning fork oscillates at a frequency of 441 Hz and the tip of each prong moves 1.8 mm to either side o...
- (II) A 0.25-kg mass at the end of a spring oscillates 3.2 times per second with an amplitude of 0.15 m. Determ...
- (II) At t = 0, an 885-g mass at rest on the end of a horizontal spring (k = 184 N/m) is struck by a hammer whi...
- (II) At t = 0, an 885-g mass at rest on the end of a horizontal spring (k = 184 N/m) is struck by a hammer whi...
- (II) A 0.25-kg mass at the end of a spring oscillates 3.2 times per second with an amplitude of 0.15 m. Determ...
- (III) A glider on an air track is connected by springs to either end of the track (Fig. 14–41). Both springs h...
- (III) A mass m is at rest on the end of a spring of spring constant k. At t = 0 it is given an impulse J by a...
- (II) At t = 0, an 885-g mass at rest on the end of a horizontal spring (k = 184 N/m) is struck by a hammer whi...