Kendall Holder

Answered

2022-01-23

P(t) models the distance of a swinging pendulum (In CM) from the place it has travelled t seconds after it starts to swing. Here, t is entered in radians.

$P\left(t\right)=-5\mathrm{cos}\left(2\pi t\right)+5$

What is the first time the pendulum reaches 3.5 CM from the place it was released?

Round your final answer to the hundredth of a second.

Ok, so I did this to get the solution:

$3.5=-5\mathrm{cos}\left(2\pi t\right)+5$

$-1.5=-5\mathrm{cos}\left(2\pi t\right)$

$0.3=\mathrm{cos}\left(2\pi t\right)$

$\mathrm{cos}-1\left(0.3\right)=2\pi t$

$\frac{{\mathrm{cos}}^{-1}\left(0.3\right)}{2\pi}=t$

The fact is this gives me 11.55 seconds to get to 3.5 CM, which does not sound right. Where did I go wrong and how can I fix it?

What is the first time the pendulum reaches 3.5 CM from the place it was released?

Round your final answer to the hundredth of a second.

Ok, so I did this to get the solution:

The fact is this gives me 11.55 seconds to get to 3.5 CM, which does not sound right. Where did I go wrong and how can I fix it?

Answer & Explanation

Fallbasisz8

Expert

2022-01-24Added 9 answers

Obviously you're expecting the input to cos in radians because you have $2\pi \text{}\text{in}\text{}\mathrm{cos}\left(2\pi t\right)$ . In physics you always use radians.

However, you can get it to work in degrees with a slight modification: change$2\pi$ to 360. Don't make it a habit though. Stay away from degrees.

However, you can get it to work in degrees with a slight modification: change

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