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Chapter 15: Q4Q (page 435)

Which of the following relationships between the acceleration a and the displacement x of a particle involve SHM: (a) a=0.5x, (b) a=400x2, (c) a=20x, (d)a=-3x2?

Short Answer

Expert verified

The relationship between acceleration and displacement is a=-20x .

Step by step solution

01

The given data 

The relationships between acceleration and position are given as:

  1. a=0.5x
  2. a=400x2
  3. a=-20x
  4. a=-3x2
02

Understanding the concept of Hooke’s law

We can use Hook鈥檚 law to determine the relation between acceleration and displacement of the particle. Comparing it with the given options, we can find the correct option showing this relationship.

Formulae:

The force on a spring due to Hooke鈥檚 law F=-kx, (i)

The force due to Newton鈥檚 second law of motion, F=ma (ii)

03

Calculation of the correct acceleration and displacement relation

ma=-kxa=-kmx

Comparing this result with the options given in the problem,

The option (c) matches with the acceleration we wrote from Hook鈥檚 law.

Therefore, the relation a=-20x involves the SHM.

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Most popular questions from this chapter

The tip of one prong of a tuning fork undergoes SHM of frequency 1000 Hzand amplitude 0.40 mm. For this tip, what is the magnitude of the (a) maximum acceleration, (b) maximum velocity, (c) acceleration at tip displacement 0.20 mm, and (d) velocity at tip displacement0.20 mm?

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

(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?

The 3.00 kgcube in Figure 15-47 has edge lengths d=6.00 cmand is mounted on an axle through its center. A spring (k=1200 N/m)connects the cube鈥檚 upper corner to a rigid wall. Initially the spring is at its rest length. If the cube is rotated 30 and released, what is the period of the resulting SHM?

A 95 kgsolid sphere with a 15 cmradius is suspended by a vertical wire. A torque of 0.20 N.mis required to rotate the sphere through an angle of 0.85 radand then maintain that orientation. What is the period of the oscillations that result when the sphere is then released?

Question: In Figure, the pendulum consists of a uniform disk with radius r = 10.cmand mass 500 gm attached to a uniform rod with length L =500mm and mass 270gm.

  1. Calculate the rotational inertia of the pendulum about the pivot point.
  2. What is the distance between the pivot point and the center of mass of the pendulum?
  3. Calculate the period of oscillation.
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