Spring-Mass System Dynamics with Hammer Impact

Chapter 11, Problem 23P

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QUESTION:

At \(t=0\), a 755-g mass at rest on the end of a horizontal spring \((k=124 \mathrm{~N} / \mathrm{m})\) is struck by a hammer, which gives the mass an initial speed of 2.96 m/s. Determine

(a) the period and frequency of the motion,

(b) the amplitude,

(c) the maximum acceleration,

(d) the position as a function of tune, and

(e) the total energy.

Questions & Answers

QUESTION:

At \(t=0\), a 755-g mass at rest on the end of a horizontal spring \((k=124 \mathrm{~N} / \mathrm{m})\) is struck by a hammer, which gives the mass an initial speed of 2.96 m/s. Determine

(a) the period and frequency of the motion,

(b) the amplitude,

(c) the maximum acceleration,

(d) the position as a function of tune, and

(e) the total energy.

ANSWER:

Solution 23P

a.)

Step 1 of 6

We have to determine the period and frequency of the motion for a 755 g mass at rest which is struck by a hammer.

The time period of motion for a spring of mass and spring constant is given by the expression,

Where,

mass of the spring

     = 755 g = 0.755 kg

spring constant = 124 N/m

Thus,

     = 0.49 s

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Spring-Mass System Dynamics with Hammer Impact
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Explore the intriguing dynamics of a spring-mass system, set in motion by a hammer's impact. Learn about period, frequency, amplitude, acceleration, position over time, and the total energy of this unique scenario.


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