Practice: A block of mass 0.300 kg is attached to a spring. At x = 0.240 m, its acceleration is ax=-12.0 m/s<sup2></sup>and its velocity is vx=4.00 m/s. What are the system’s (a) force constant k and (b) amplitude of motion?

Subjects

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Spring Force (Hooke's Law) | 15 mins | 0 completed | Learn |

Intro to Simple Harmonic Motion (Horizontal Springs) | 32 mins | 0 completed | Learn |

Energy in Simple Harmonic Motion | 22 mins | 0 completed | Learn |

Simple Harmonic Motion of Vertical Springs | 20 mins | 0 completed | Learn |

Simple Harmonic Motion of Pendulums | 32 mins | 0 completed | Learn |

Energy in Pendulums | 16 mins | 0 completed | Learn |

Practice: A block of mass 0.300 kg is attached to a spring. At x = 0.240 m, its acceleration is ax=-12.0 m/s<sup2></sup>and its velocity is vx=4.00 m/s. What are the system’s (a) force constant k and (b) amplitude of motion?

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Concept #1: Energy in Simple Harmonic Motion

Example #1: Example

Practice #1: Practice

Example #2: Example

A 2.00-kg, frictionless block is attached to an ideal spring with force constant 300 N/m. At t = 0 the block has velocity -4.00 m/s and displacement +0.200 m.Find (a) the amplitude and (b) the phase angle Write an equation for the position as a function of time. Assume x(t) in meters and t in seconds.

The graph on the next page shows the displacement of the block as a function of time (this is the same mass-spring situation as problem 1 but with a different mass). The maximum displacement is 15 cm. (The graph for this exercise is provided at the end of this lab on page 7. For your records, trace your solutions from your completed graphs into your lab notebook, copy your solution, and fasten the copy into your notebook.) a) If k = 150 N/m, calculate the mass of the block. b) Draw the graphs for velocity and acceleration of the motion. On the graphs, label the maximum values of velocity and acceleration, respectively. c) Draw the graph for kinetic energy and calculate and label on the graph the maximum value of KEd) Draw the graph for the elastic potential energy and calculate and label on the graph the maximum value of the elastic PE.e) Calculate the numerical value and draw the graph for the total energy.

A 750g mass is placed on a spring which lies on a frictionless surface. The spring has a spring constant k=500 N/m and is at its equilibrium length.(a) The spring is stretched so that it is 10.0 cm longer than its equilibrium length. How much elastic potential energy is stored in the spring now?(b) Now the spring from part (a) is released. What is the speed of the mass as it passes through the equilibrium point (x=0)?

A harmonic oscillator has angular frequency ω and amplitude A.(a) How often is elastic potential energy is equal to the kinetic energy in each cycle?(b) What is the time between occurrences?

In simple harmonic motion, the speed is greatest at that point in the cycle whenA) the magnitude of the acceleration is a maximum.B) the displacement is a maximum.C) the magnitude of the acceleration is a minimum.D) the potential energy is a maximum.E) the kinetic energy is a minimum.

Suppose the damping constant b of an oscillator increases. a. Is the medium more resistive or less resistive?b. Do the oscillations damp out more quickly or less quickly? c. Is the time constant, τ increased, or decreased?

Learning Goal: To learn to apply the law of conservation of energy to the analysis of harmonic oscillators.Systems in simple harmonic motion, or harmonic oscillators, obey the law of conservation of energy just like all other systems do. Using energy considerations, one can analyze many aspects of motion of the oscillator.Find the kinetic energy K of the block at the moment labeled B. Express your answer in terms of k and A.

A massless spring (with force constant k = 188 N/m) connects a wall and a block of wood. The system is initially at rest, with the spring unstretched. The block has mass M = 58.5 g and is able to move without friction on a table. A gun is positioned to fire a bullet of mass m = 7.1 g into the block along the spring axis. After the gun is fired, the bullet gets embedded in the block, and the spring is compressed a maximum distance d = 0.99 m.Part (a) Find an equation for the speed of the bullet v, just before it hits the block, in terms of the variables given statement.Part (b) In meters per second, what is the speed of the bullet v before it enters the block?Part (c) What is the frequency f (in Hz) of the resulting periodic motion of the block/bullet and spring system?

An object of mass m attached to a spring of force constant k oscillates with simple harmonic motion. The maximum displacement from equilibrium is A and the total mechanical energy of the system is E.What is the object's velocity when its potential energy is 2/3E?Answer in terms of m, k, A

How is simple harmonic motion similar and different from that of a ball bouncing on a hard floor? (HINT: one similarity and two differences)

Consider the block in the process of oscillating.If the kinetic energy of the block is increasing, the block must bea) at the equilibrium position.b) at the amplitude displacementc) moving to the right.d) moving to the left.e) moving away from equilibrium.f) moving toward equilibrium.

A harmonic oscillator has angular frequency ω and amplitude A.What are the magnitudes of the displacement and velocity when the elastic potential energy is equal to the kinetic energy? (Assume that U = 0 at equilibrium.) (Use any variable or symbol stated above as necessary.)x =v =

A harmonic oscillator has angular frequency ω and amplitude A.At an instant when the displacement is equal to A/2, what fraction of the total energy of the system, E, is kinetic, and what fraction is potential?

A mass is oscillating with amplitude A at the end of a spring. How far (in terms of A) is this mass from the equilibrium position of the spring when the elastic potential energy equals the kinetic energy?

The amplitude of a lightly damped harmonic oscillator decreases by 3.0% during each cycle. What percentage of the mechanical energy of the oscillator is lost in each cycle?

An object of mass m is attached to a spring having force constant k. The object oscillates with simple harmonic motion. Its maximum displacement from equilibrium is A. What is the total mechanical energy of the spring/mass system when the object is located at x = +A

An object of mass m attached to a spring of force constant K oscillates with simple harmonic motion. The maximum displacement from equilibrium is A and the total mechanical energy of the system is E.What is the system's potential energy when its kinetic energy is equal to 3/4E?

Which of the following are proper expressions for the total energy of an object in SHM?

At what displacement of a SHO is the energy half kinetic and half potential?Express your answer in terms of amplitude A.

The amplitude of a lightly damped oscillator decreases by 3.0 % during each cycle. What percentage of the mechanical energy of the oscillator is lost in each cycle?

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