Question

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

Answer 1

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

Answer 2

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

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

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Further explanation

Let's recall Elastic Potential Energy formula as follows:

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

where:

Ep = elastic potential energy ( J )

k = spring constant ( N/m )

x = spring extension ( compression ) ( m )

Let us now tackle the problem!

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Given:

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

Asked:

A. velocity = v = ?

B. spring constant = k = ?

Solution:

Question A:

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

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

$v = -20 \sin 10t$

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

$v = -20 \sin (4.0)$

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

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Question B:

$k = m \omega^2$

$k = 0.05 \times 10^2$

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

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Learn more

• 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

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Answer details

Grade: High School

Subject: Physics

Chapter: Elasticity