Mysterious22
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#1
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#1
A mass is attached to the end of a spring the displacement of the pass in cm from the origin O at t (s) is given by the formula
s(t) =-16 -1.4cos (126t)

A) work out the minimum distance of the mass from the origin

B) how long does it take for the pass to complete 7 full oscillations

I don't really understand and don't know what to do at all

Pls help I'm so. Confused
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AstroST
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#2
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#2
(Original post by Mysterious22)
A mass is attached to the end of a spring the displacement of the pass in cm from the origin O at t (s) is given by the formula
s(t) =-16 -1.4cos (126t)

A) work out the minimum distance of the mass from the origin

B) how long does it take for the pass to complete 7 full oscillations

I don't really understand and don't know what to do at all

Pls help I'm so. Confused
For A) Think about the possible values of cos and so what the closest possible value of s(t) to 0 will be.

For B), a cos function completes a full oscillation when it's argument (the bit inside the brackets) is 2pi. So you can use that to work out the period of the mass.
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Shadowdraconis
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#3
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#3
(Original post by AstroST)
For A) Think about the possible values of cos and so what the closest possible value of s(t) to 0 will be.

For B), a cos function completes a full oscillation when it's argument (the bit inside the brackets) is 2pi. So you can use that to work out the period of the mass.
I still don't get how to approach this. I tried setting the time t to 0 but that doesn't work and I also tried to solve it like an equation that also doesn't work. I'm so stuck on this I want to cry please someone help.
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Prasiortle
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#4
Report 3 years ago
#4
(Original post by Shadow_12)
I still don't get how to approach this. I tried setting the time t to 0 but that doesn't work and I also tried to solve it like an equation that also doesn't work. I'm so stuck on this I want to cry please someone help.
(a) Cosine is bounded between -1 and 1 (think of the graph), so -1 <= cos(126t) <= 1, so -1.4 <= 1.4cos(126t) <= 1.4, so -16-1.4 <= -16-1.4cos(126t) <= -16+1.4, so the displacement is between -17.4 and -14.6, and thus the minimum distance is 14.6 metres.

(b) A full oscillation goes from 0 to 2pi on the cosine graph, so for 7 full oscillations, it must go from 0 to 7*2pi = 14pi. Thus we set the argument of cosine equal to 14pi, giving 126t = 14pi, so t = pi/9 seconds.
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Shadowdraconis
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#5
Report 3 years ago
#5
(Original post by Prasiortle)
(a) Cosine is bounded between -1 and 1 (think of the graph), so -1 <= cos(126t) <= 1, so -1.4 <= 1.4cos(126t) <= 1.4, so -16-1.4 <= -16-1.4cos(126t) <= -16+1.4, so the displacement is between -17.4 and -14.6, and thus the minimum distance is 14.6 metres.

(b) A full oscillation goes from 0 to 2pi on the cosine graph, so for 7 full oscillations, it must go from 0 to 7*2pi = 14pi. Thus we set the argument of cosine equal to 14pi, giving 126t = 14pi, so t = pi/9 seconds.
Ohh ok... I think I get it now thanks so much!!! Ur a lifesaver!!
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