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Chapter 15: Q32P (page 437)

Figure shows the kinetic energy Kof a simple harmonic oscillator versus its position . The vertical axis scale is set by Ks=4.0J. What is the spring constant?

Short Answer

Expert verified

The spring constant of a simple harmonic oscillator is 8.33×102N/m.

Step by step solution

01

The given data

From graph, we can say that,

  1. Total energy of the system E = 6.0 J,
  2. The amplitude of the oscillation, Xm=12cmor0.12m.
02

Understanding the concept of motion

Using the given graph we can find the total energy and amplitude of motion, so we can find the spring constant.

Formula:

The energy of the system of the harmonic oscillator,

E=12kxm2...(1)

03

Calculation of spring constant

Using equation (i) and the given values, we get the spring constant as given:

6.012k(0.12)2k=8.33×102N/m

The value of the spring constant is8.33×102N/m .

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Most popular questions from this chapter

The physical pendulum in Fig. 15-62 has two possible pivot points A and B. Point A has a fixed position but B is adjustable along the length of the pendulum as indicated by the scaling. When suspended from A, the pendulum has a period ofT=1.80s. The pendulum is then suspended from B, which is moved until the pendulum again has that period. What is the distance L between A and B?

Question: The angle of the pendulum in Figure is given by θ=θmcos[(4.44rad/s)t+Φ]. If at t = 0θ=0.040rad , anddθ/dt=0.200rad/s ,

  1. what is the phase constant φ,
  2. what is the maximum angleθm ?

(Hint: Don’t confuse the rate dθat which changes with the θof the SHM.)

A10gparticle undergoes SHM with amplitude of 2.0mm, a maximum acceleration of magnitude8.0×103m/s2, and an unknown phase constantϕ.

(a) What is the period of the motion?

(b) What is the maximum speed of the particle?

(d) What is the total mechanical energy of the oscillator?

What is the magnitude of the force on the particle when the particle is at

(d) its maximum displacement and

(e) Half its maximum displacement?

Question: In Figure, a physical pendulum consists of a uniform solid disk (of radius R = 2.35 cm ) supported in a vertical plane by a pivot located a distance d = 1.75 cm from the center of the disk. The disk is displaced by a small angle and released. What is the period of the resulting simple harmonic motion?

A massless spring hangs from the ceiling with a small object attached to its lower end. The object is initially held at rest in a position yisuch that the spring is at its rest length. The object is then released from yiand oscillates up and down, with its lowest position being 10cmbelowyi

(a) What is the frequency of the oscillation?

(b) What is the speed of the object when it is 8.0cmbelow the initial position?

(c) An object of mass 300gis attached to the first object, after which the system oscillates with half the original frequency. What is the mass of the first object?

(d) How far below yiis the new equilibrium (rest) position with both objects attached to the spring?
See all solutions

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