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Chapter 4: Q57P (page 168)

A vertical mass-spring oscillator has an amplitude of 0.06m and a period of 0.4s. (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 is0.94m/s.

b) The maximum acceleration of the mass is14.8m/s2.

Step by step solution

01

Identification of given data

Given data can be listed below,

  • Amplitude, A=0.06m

  • Period, T=0.4s

02

Evaluating angular frequency of the mass-spring system

Expression for the period of oscillation is given as,

T=2πωω=2πT

Substituting 0.4sfor T in the above equation

ω=2π0.4=15.7rad/s

03

Evaluating maximum speed of mass

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

ωmax=A

Substituting 0.06mfor A, 15.7rad/sfor ωin the above equation,

vmax=0.06×15.7=0.94m/s

04

Evaluating maximum acceleration of mass

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

ωmax=Aω2

Substituting 0.06mfor A, 15.7rad/sfor ωin the above equation,

ωmax=0.06×15.72=14.8m/s2

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Most popular questions from this chapter

Two metal rods are made of different elements. The interatomic spring stiffness of element A is three times larger than the interatomic spring stiffness for element B. The mass of an atom of element A is three times greater than the mass of an atom of element B. The atomic diameters are approximately the same for A and B. What is the ratio of the speed of sound in rod A to the speed of sound in rod B?

One mole of tungsten (6.02×1023atoms) has a mass of 184 g, as shown in the periodic table on the inside front cover of the textbook. The density of tungsten is19.3g/cm3. 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.

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