Simple Harmonic MotionView Image.Kindly answer: d,e,f 1. A 1.50 kg mass on a spring has displacement as a function of time given byx(t) = (7.40 cm) cos [(4.16 rad/s)t – 2.42]Find (a) the time for one complete vibration; (b) the force constant of the spring;(c) the maximum speed of the mass; (d) the maximum force on the mass;(e) the position, speed, and acceleration of the mass at t= 1.00 s;(f) the force on the mass at that time. The time for one complete vibration is:2.7T =-274.16 rad/s=1.51s(b)The force constant of the spring is:k = mo=(1.50 kg)(4.16 rad/s)= 25.9584 N/m- 25.96 N/mStep 3(c)The maximum speed of the mass is:= Ao=(7.40 cm )(4.16 rad/s)mar=(0.074 m)(4.16 rad/s)= 0.30784 m/s- 0.31 m/s

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Answered: 1. A 1.50 kg mass on a spring has…

Physics for Scientists and Engineers with Modern Physics

10th Edition

ISBN:9781337553292

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter15: Oscillatory Motion

Section: Chapter Questions

Problem 27P

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Simple Harmonic Motion

View Image.

Kindly answer: d,e,f

1. A 1.50 kg mass on a spring has displacement as a function of time given by
x(t) = (7.40 cm) cos [(4.16 rad/s)t – 2.42]
Find (a) the time for one complete vibration; (b) the force constant of the spring;
(c) the maximum speed of the mass; (d) the maximum force on the mass;
(e) the position, speed, and acceleration of the mass at t= 1.00 s;
(f) the force on the mass at that time.

The time for one complete vibration is:
2.7
T =-
27
4.16 rad/s
=1.51s
(b)
The force constant of the spring is:
k = mo
=(1.50 kg)(4.16 rad/s)
= 25.9584 N/m
- 25.96 N/m
Step 3
(c)
The maximum speed of the mass is:
= Ao
=(7.40 cm )(4.16 rad/s)
mar
=(0.074 m)(4.16 rad/s)
= 0.30784 m/s
- 0.31 m/s

Definition Definition Special type of oscillation where the force of restoration is directly proportional to the displacement of the object from its mean or initial position. If an object is in motion such that the acceleration of the object is directly proportional to its displacement (which helps the moving object return to its resting position) then the object is said to undergo a simple harmonic motion. An object undergoing SHM always moves like a wave.

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