17. Periodic Motion

Intro to Simple Harmonic Motion (Horizontal Springs)

Simple Harmonic Motion Derivations using Calculus (Mass-Spring System)

Anderson Video - Period of an Oscillating Spring

Anderson Video - Cosine Solution to Simple Harmonic Motion

A 2.40-kg ball is attached to an unknown spring and allowed to oscillate. Figure E14.7 <img src="https://lightcat-files.s3.amazonaws.com/problem_images/c0d7dfabd9f43c43-1671729735728.jpg" alt="" /> shows a graph of the ball’s position x as a function of time t. What are the oscillation’s (a) period, (b) frequency, (c) angular frequency, and (d) amplitude? (e) What is the force constant of the spring?<img class="fr-dib" src="https://lightcat-files.s3.amazonaws.com/problem_images/5f7b437db1fdf68c-1678286842922.jpg" style="width: 300px;">

Anderson Video - Spring Example- Max Speed and Acceleration

Example

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.

A certain astronaut oscillates back and forth on a chair attached to springs. The spring constants are such that when her mass is known to be <math display=“inline”><mrow><mn>55</mn><mo>.</mo><mrow><mn>0</mn><mo rspace="thickmathspace">&#x2062;</mo><mi mathvariant="normal" class="MathML-Unit">kg</mi></mrow><mo>,</mo></mrow></math> she oscillates with a period of <math display=“inline”><mrow><mn>2</mn><mo>.</mo><mrow><mn>85</mn><mo rspace="thickmathspace">&#x2062;</mo><mi mathvariant="normal" class="MathML-Unit">s</mi></mrow><mo>.</mo></mrow></math> After some time in space, a repetition of the measurement yields a period of <math display=“inline”><mrow><mn>2</mn><mo>.</mo><mrow><mn>75</mn><mo rspace="thickmathspace">&#x2062;</mo><mi mathvariant="normal" class="MathML-Unit">s</mi></mrow><mo>.</mo></mrow></math> What is the astronaut’s mass now?

A 250 g air-track glider attached to a spring oscillates with maximum speed of <math display=“inline”><mrow><mn>0</mn><mo>.</mo><mn>97</mn><mo rspace="thickmathspace">&#x2062;</mo><mrow><mfrac bevelled="true"><mi mathvariant="normal" class="MathML-Unit">m</mi><mi mathvariant="normal" class="MathML-Unit">s</mi></mfrac></mrow></mrow></math>. If the spring has a spring constant of <math display=“inline”><mrow><mn>450</mn><mo rspace="thickmathspace">&#x2062;</mo><mrow><mfrac bevelled="true"><mi mathvariant="normal" class="MathML-Unit">N</mi><mi mathvariant="normal" class="MathML-Unit">m</mi></mfrac></mrow></mrow></math>, at what distance from the equilibrium position will the glider have a speed of <math display=“inline”><mrow><mn>0</mn><mo>.</mo><mn>43</mn><mo rspace="thickmathspace">&#x2062;</mo><mrow><mfrac bevelled="true"><mi mathvariant="normal" class="MathML-Unit">m</mi><mi mathvariant="normal" class="MathML-Unit">s</mi></mfrac></mrow></mrow></math>?

Anderson Video - Simple Harmonic Motion

Anderson Video - Graphing Simple Harmonic Motion and Determining Phi

How To Solve Simple Harmonic Motion Problems In Physics

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?

Simple Harmonic Motion: Crash Course Physics #16

A small block is attached to an ideal spring and is moving in SHM on a horizontal, frictionless surface. When the amplitude of the motion is 0.090 m, it takes the block 2.70 s to travel from x = 0.090 m to x = -0.090 m. If the amplitude is doubled, to 0.180 m, how long does it take the block to travel (a) from x = 0.180 m to x = -0.180 m?

Anderson Video - Speed of a Block on a 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 start it oscillating. The elapsed time from when the glider first moves through the equilibrium point to the second time it moves through that point is 2.60 s. Find the spring’s force constant.

The displacement of an oscillating object as a function of time is shown in Fig. E14.4 <img src="https://lightcat-files.s3.amazonaws.com/problem_images/1e367daa99e0088e-1671566749963.jpg" alt="" />. What is (a) the frequency? (b) the amplitude? (c) the period? (d) the angular frequency of this motion?<img class="fr-dib" src="https://lightcat-files.s3.amazonaws.com/problem_images/cc853416a1171e44-1678285010203.jpg" style="width: 293px;">

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?

A 2.40-kg ball is attached to an unknown spring and allowed to oscillate. Figure E14.7 <img src="https://lightcat-files.s3.amazonaws.com/problem_images/e4ad93cf34fc556a-1671729118522.jpg" alt="" /> shows a graph of the ball’s position x as a function of time t. What are the oscillation’s (a) period, (b) frequency, (c) angular frequency, and (d) amplitude? (e) What is the force constant of the spring?<img class="fr-dib" src="https://lightcat-files.s3.amazonaws.com/problem_images/21893aa1fba7ea77-1678285085773.jpg" style="width: 300px;">

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?

Physics - Mechanics: Ch 16.5 Simple Harmonic Motion-2 Springs (1 of 5) 2 Equal Springs, 1 Mass

An air-track glider attached to a spring oscillates between the 50 cm mark and the 62 cm mark. It completes seven oscillations in 10 s. What is the maximum speed of the glider as it oscillates?

Equations of Simple Harmonic Motion

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 - (pi/2)]. What are (a) the period; (b) the amplitude; (c) the maximum acceleration of the mass; (d) the force constant of the spring?

Simple Harmonic Motion 2 - Mass on a horizontal spring

A 2.00-kg, frictionless block is attached to an ideal spring with force constant 300 N/m. At t = 0 the spring is neither stretched nor compressed and the block is moving in the negative direction at 12.0 m/s. Find (a) the amplitude and (b) the phase angle. (c) Write an equation for the position as a function of time.

Intro to Simple Harmonic Motion

A small block is attached to an ideal spring and is moving in SHM on a horizontal, frictionless surface. When the amplitude of the motion is 0.090 m, it takes the block 2.70 s to travel from x = 0.090 m to x = -0.090 m. If the amplitude is doubled, to 0.180 m, how long does it take the block to travel (b) from x = 0.090 m to x = -0.090 m?

Weighing Astronauts. This procedure has been used to “weigh” astronauts in space: A 42.5-kg chair is attached to a spring and allowed to oscillate. When it is empty, the chair takes 1.30 s to make one complete vibration. But with an astronaut sitting in it, with her feet off the floor, the chair takes 2.54 s for one cycle. What is the mass of the astronaut?

The wings of the blue-throated hummingbird (Lampornis clemenciae), which inhabits Mexico and the southwestern United States, beat at a rate of up to 900 times per minute. Calculate (a) the period of vibration of this bird’s wings, (b) the frequency of the wings’ vibration, and (c) the angular frequency of the bird’s wing beats.

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 its position and velocity components are +1.1 cm and -15 cm/s, respectively. (a) Find the acceleration component of the needle at t = 0.

Energy in Horizontal Springs Example

(a) Music. When a person sings, his or her vocal cords vibrate in a repetitive pattern that has the same frequency as the note that is sung. If someone sings the note B flat, which has a frequency of 466 Hz, how much time does it take the person’s vocal cords to vibrate through one complete cycle, and what is the angular frequency of the cords?

A machine part is undergoing SHM with a frequency of 4.00 Hz and amplitude 1.80 cm. How long does it take the part to go from x = 0 to x = -1.80 cm ?

The displacement of an oscillating object as a function of time is shown in Fig. E14.4 <img src="https://lightcat-files.s3.amazonaws.com/problem_images/26fd86d16c7e7888-1671566047601.jpg" alt="" />. What is (a) the frequency? (b) the amplitude? (c) the period? (d) the angular frequency of this motion?<img class="fr-dib" src="https://lightcat-files.s3.amazonaws.com/problem_images/887bed682afd2a09-1678285012146.jpg" style="width: 290px;">

Simple Harmonic Motion Introduction(SHM) via a Horizontal Mass-Spring System

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 and is instantaneously at rest. Calculate the time it takes the object to go (a) from x = 0.320 m to x = 0.160 m. (b) from x = 0.160 m to x = 0.

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