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Chapter 4: Q57P (page 168)

A vertical mass-spring oscillator has an amplitude of $0.06 m$ and a period of $0.4 s$ . (a) What is the maximum speed of the mass? (b) What is the maximum acceleration of the mass?

Short Answer

Expert verified

a) The maximum speed of the mass is $0.94 m / s$ .

b) The maximum acceleration of the mass is $14.8 m / s^{2}$ .

Step by step solution

01

Identification of given data

Given data can be listed below,

Amplitude, $A = 0.06 m$
Period, $T = 0.4 s$

02

Evaluating angular frequency of the mass-spring system

Expression for the period of oscillation is given as,

$T = \frac{2 蟺}{蝇} 蝇 = \frac{2 蟺}{T}$

Substituting $0.4 s$ for $T$ in the above equation

$蝇 = \frac{2 蟺}{0.4} = 15.7 r a d / s$

03

Evaluating maximum speed of mass

Expression for the maximum speed of the spring-mass system is

$蝇_{m a x} = A$

Substituting $0.06 m$ for $A$ , $15.7 r a d / s$ for $蝇$ in the above equation,

$v_{m a x} = 0.06 脳 15.7 = 0.94 m / s$

04

Evaluating maximum acceleration of mass

Expression for the maximum acceleration of the spring-mass system is,

$蝇_{m a x} = A 蝇^{2}$

Substituting $0.06 m$ for $A$ , $15.7 r a d / s$ for $蝇$ in the above equation,

$蝇_{m a x} = 0.06 脳 15 . 7^{2} = 14.8 m / s^{2}$

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Most popular questions from this chapter

Forty-five identical springs are placed side by side (in parallel) and connected to a large massive block. The stiffness of the 45-spring combination is 20,250N/m. What is the stiffness of one of the individual springs?

One mole of tungsten ( $6.02 脳 10^{23}$ atoms) has a mass of 184 g, as shown in the periodic table on the inside front cover of the textbook. The density of tungsten is $19.3 g / {cm}^{3}$ . What is the approximate diameter of a tungsten atom (length of a bond) in a solid block of the material? Make the simplifying assumption that the atoms are arranged in a cubic array.

In outer space, a rod is pushed to the right by a constant force F (Figure 4.54). Describe the pattern of interatomic distances along the rod. Include a specific comparison of the situation at locations A, B, and C. Explain briefly in terms of fundamental principles.

Figure 4.54

Hint: Consider the motion of an individual atom inside the rod, and various locations along the rod.

(b) After the rod in part (a) reaches a speed v, the object that had been exerting the force on the rod is removed. Describe the subsequent motion of the rod and the pattern of interatomic distances inside the rod. Include a specific comparison of the situation at locations A, B, and C. Explain briefly.

A spring suspended vertically is $18 c m$ long. When you suspend a $30 g$ weight from the spring, at rest, the spring is $22 c m$ long. Next you pull down on the weight so the spring is $23 c m$ long and you release the weight from rest. What is the period of oscillation?

A bouncing ball is an example of an anharmonic oscillator. If you quadruple the maximum height, what happens to the period? (Assume that the ball keeps returning almost to the same height.)

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