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Chapter 4: Q53P (page 168)

Here on Earth you hang a mass from a vertical spring and start it oscillating with amplitude1.7cm. You observe that it takes 2.1sto make one round-trip. You construct another vertical oscillator with a mass 6 times as heavy and a spring 10 times as stiff. You take it to a planet wheregplanet=6.8N/kg.You start oscillating with amplitude3.3cm. How long does it take for the mass to make one round-trip?

Short Answer

Expert verified

The periodT'=1.627s it takes for the mass to make one round trip.

Step by step solution

01

Identification of given data

Given data can be listed below,

  • Amplitude, A=1.7cm

  • Time, t=2.1s

Acceleration due to the gravity of the planet,gplanet=6.8N/kg

02

Calculating angular frequency

Expression for angular frequency of the spring-mass system is given by

蝇=km

Our construction spring-mass system and the angular frequency are given by

蝇'=k'm'=10k6m=1.29km=1.29蝇

03

Period of our constructing spring-mass system

The expression for the period of the spring-mass system is given by

蝇=2蟺f=2蟺TT=2蟺蝇

The period of the oscillator does not depend on gravity as the measurement of horizontal spring.

From the period of our construction spring-mass system is given by

T'=2蟺蝇'

Now from the above equation, we can write as

T蝇=2蟺T'=T蝇1.29蝇=2.1脳11.29=1.627s

Thus, the periodT'=1.627sit takes for the mass to make one round trip.

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