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Simple Harmonic Motion of an oscillating particle

  • Thread starter maniacp08
  • Start date
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The period of an oscillating particle is 56 s, and its amplitude is 18 cm. At t = 0, it is at its equilibrium position. Find the distances traveled during these intervals.
(a) t = 0 to t = 14 s
cm

(b) t = 14 s to t = 28 s
cm

(c) t = 0 to t = 7 s
cm

(d) t = 7 s to t = 14 s
cm

x = Acos([tex]\omega[/tex] * t * [tex]\delta[/tex])
[tex]\omega[/tex] = 2[tex]\pi[/tex] / T
[tex]\omega[/tex] = 2[tex]\pi[/tex] / 56

Since x = 0 when t = 0
Then [tex]\delta[/tex] = [tex]\pi[/tex] / 2
correct?

for part A)

x = 18cm * cos[2[tex]\pi[/tex] / 56 * 14s + [tex]\pi[/tex] / 2] - cos[2[tex]\pi[/tex] / 56 * 0s + [tex]\pi[/tex] / 2]

Is this good?
1. Homework Statement



2. Homework Equations



3. The Attempt at a Solution
 

Answers and Replies

alphysicist
Homework Helper
2,238
1
Hi maniacp08,

The period of an oscillating particle is 56 s, and its amplitude is 18 cm. At t = 0, it is at its equilibrium position. Find the distances traveled during these intervals.
(a) t = 0 to t = 14 s
cm

(b) t = 14 s to t = 28 s
cm

(c) t = 0 to t = 7 s
cm

(d) t = 7 s to t = 14 s
cm

x = Acos([tex]\omega[/tex] * t * [tex]\delta[/tex])
[tex]\omega[/tex] = 2[tex]\pi[/tex] / T
[tex]\omega[/tex] = 2[tex]\pi[/tex] / 56

Since x = 0 when t = 0
Then [tex]\delta[/tex] = [tex]\pi[/tex] / 2
correct?

for part A)

x = 18cm * cos[2[tex]\pi[/tex] / 56 * 14s + [tex]\pi[/tex] / 2] - cos[2[tex]\pi[/tex] / 56 * 0s + [tex]\pi[/tex] / 2]
The 18cm needs to multiply both cosine functions, not just the first one. Was that just a typo?

Also you can think about how the time period of 14 seconds is related to the period, to get the answer right away.
 

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