0. Math Review

1. Intro to Physics Units

2. 1D Motion / Kinematics

3. Vectors

4. 2D Kinematics

5. Projectile Motion

6. Intro to Forces (Dynamics)

7. Friction, Inclines, Systems

8. Centripetal Forces & Gravitation

9. Work & Energy

10. Conservation of Energy

11. Momentum & Impulse

12. Rotational Kinematics

13. Rotational Inertia & Energy

14. Torque & Rotational Dynamics

15. Rotational Equilibrium

16. Angular Momentum

17. Periodic Motion

18. Waves & Sound

19. Fluid Mechanics

20. Heat and Temperature

21. Kinetic Theory of Ideal Gases

22. The First Law of Thermodynamics

23. The Second Law of Thermodynamics

24. Electric Force & Field; Gauss' Law

25. Electric Potential

26. Capacitors & Dielectrics

27. Resistors & DC Circuits

28. Magnetic Fields and Forces

29. Sources of Magnetic Field

30. Induction and Inductance

31. Alternating Current

32. Electromagnetic Waves

33. Geometric Optics

34. Wave Optics

36. Special Relativity

[BOOK PHYS] !CLUTCH

Physics - Mechanics: Simple Harmonic Motion (3 of 5) Mass on Spring

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

Oscillations Demo: Mass Spring System

Simple harmonic motion - vertical spring

A spring is hanging from the ceiling. Attaching a 500 g physics book to the spring causes it to stretch 20 cm in order to come to equilibrium.

c. What is the book's maximum speed?

A chair of mass 30 kg on top of a spring oscillates with a period of 2s. (a) Find the spring's force constant. You place an object on top of the chair, and it now oscillates with a period of 3s. (b) Find the object's mass.

A spring is hung from the ceiling. When a block is attached to its end, it stretches 2.0 cm before reaching its new equilibrium length. The block is then pulled down slightly and released. What is the frequency of oscillation?

Simple Harmonic Motion of Vertical Springs

Your lab instructor has asked you to measure a spring constant using a dynamic method—letting it oscillate—rather than a static method of stretching it. You and your lab partner suspend the spring from a hook, hang different masses on the lower end, and start them oscillating. One of you uses a meter stick to measure the amplitude, the other uses a stopwatch to time 10 oscillations. Your data are as follows:

<img src="https://lightcat-files.s3.amazonaws.com/problem_images/9838bb0f67e594c7-1679567665279.jpg" alt="" />

Use the best-fit line of an appropriate graph to determine the spring constant.

A <math display='inline'><mrow><mn>2</mn><mo>.</mo><mrow><mn>0</mn><mo rspace="thickmathspace">&#x2062;</mo><mi mathvariant="normal" class="MathML-Unit">kg</mi></mrow></mrow></math> block is gently lowered onto a vertical spring, and the spring compresses <math display='inline'><mrow><mn>5</mn><mo>.</mo><mrow><mn>0</mn><mo rspace="thickmathspace">&#x2062;</mo><mi mathvariant="normal" class="MathML-Unit">cm</mi></mrow><mo>.</mo></mrow></math> Another block is added, and the spring compresses an additional <math display='inline'><mrow><mn>3</mn><mo>.</mo><mrow><mn>0</mn><mo rspace="thickmathspace">&#x2062;</mo><mi mathvariant="normal" class="MathML-Unit">cm</mi></mrow><mo>.</mo></mrow></math> What is the mass of the second block added?

Solution  to Problem #78, Vertical Spring

A spring with spring constant <math><mrow><mn>2500</mn><mtext></mtext><mtext>&#x00A0;N/m</mtext></mrow></math> has one end connected to the ceiling and the other end fastened to a <math display='inline'><mrow><mn>3</mn><mo>.</mo><mrow><mn>0</mn><mo rspace="thickmathspace">&#x2062;</mo><mi mathvariant="normal" class="MathML-Unit">kg</mi></mrow></mrow></math> mass. The mass is oscillating with amplitude 3.0 cm. How fast is the mass moving when it is <math display='inline'><mrow><mn>2</mn><mo>.</mo><mrow><mn>0</mn><mo rspace="thickmathspace">&#x2062;</mo><mi mathvariant="normal" class="MathML-Unit">cm</mi></mrow></mrow></math> above the equilibrium position?

Simple Harmonic Motion 3 - Mass on a vertical spring

Vertical Springs | Simple Harmonic Motion | AP Physics C

Example

A spring with spring constant 15 N/m hangs from the ceiling. A ball is attached to the spring and allowed to come to rest. It is then pulled down 6.0 cm and released. If the ball makes 30 oscillations in 20 s, what are its (a) mass and (b) maximum speed?

A spring is hanging from the ceiling. Attaching a 500 g physics book to the spring causes it to stretch 20 cm in order to come to equilibrium.

b. From equilibrium, the book is pulled down 10 cm and released. What is the period of oscillation?

A 200 g block hangs from a spring with spring constant 10 N/m. At t = 0 s the block is 20 cm below the equilibrium point and moving upward with a speed of 100 cm/s. What are the block's

a. Oscillation frequency?

A compact car has a mass of 1200 kg. Assume that the car has one spring on each wheel, that the springs are identical, and that the mass is equally distributed over the four springs.

b. What will be the car's oscillation frequency while carrying four 70 kg passengers?

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