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3 years ago

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A complete description of simple harmonic motion must take into account several physical quantities and various mathematical rel

ations among them. This information is needed to solve oscillation problems of this type.The position of a 50 g oscillating mass is given by x(t)=(2.0cm)cos(10t), where t is in seconds.Part ADetermine the velocity at t=0.40s.Part BAssume that the oscillating mass described in Part A is attached to a spring. What would the spring constant k of this spring be?

2 answers:

vazorg [7]3 years ago

8 0

Answer:

Explanation:

x = 2 cos wt = 2 cos 10t ; w = 10

velocity = dx/dt = -2 x 10 sin 10 t.=- 20 sin 10t

t = .4

velocity = -20 sin 10 x .4 = -20 sin 4 = -20 x -0.7568 = 15.136 cm /s

w = √ k / m = 10 = √ k / .05

k = 15.136 N/m

NemiM [27]3 years ago

3 0

A. the velocity at t = 0.40 s is about 15 cm/s

B. the spring constant k is about 5.0 N/m

$\texttt{ }$

<h3>Further explanation</h3>

Let's recall Elastic Potential Energy formula as follows:

$\boxed{E_p = \frac{1}{2}k x^2}$

where:

<em>Ep = elastic potential energy ( J )</em>

<em>k = spring constant ( N/m )</em>

<em>x = spring extension ( compression ) ( m )</em>

Let us now tackle the problem!

$\texttt{ }$

<u>Given:</u>

oscillating mass = m = 50 g = 0.05 kg

amplitude = A = 2.0 cm

angular frequency = ω = 10 rad/s

time taken = t = 0.40 s

<u>Asked:</u>

A. velocity = v = ?

B. spring constant = k = ?

<u>Solution:</u>

<h3>Question A:</h3>

$v = \frac{dx}{dt}$

$v = \frac{d}{dt} (2.0 \cos 10t)$

$v = -20 \sin 10t$

$v = -20 \sin 10(0.40)$

$v = -20 \sin (4.0)$

$\boxed{v \approx 15 \texttt { cm/s}}$

$\texttt{ }$

<h3>Question B:</h3>

$k = m \omega^2$

$k = 0.05 \times 10^2$

$\boxed{k = 5.0 \texttt{ N/m}}$

$\texttt{ }$

<h3>Learn more</h3>

Kinetic Energy : brainly.com/question/692781

Acceleration : brainly.com/question/2283922

The Speed of Car : brainly.com/question/568302
Young Modulus : brainly.com/question/9202964
Simple Harmonic Motion : brainly.com/question/12069840

$\texttt{ }$

<h3>Answer details</h3>

Grade: High School

Subject: Physics

Chapter: Elasticity

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<h3>a.</h3>

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