- #1
Moonflower
- 21
- 0
Calculus Logarithmic Functions help please!
The question is:
A particle moves alonge the x-axis with position at time t given by x(t) = e^(-t) sin t for 0 ≤ t ≤ 2π.
1. Find the time t at which the particle is farthest to the left. Justify your answer.
2. Find the value of the constant A for which x(t) satisfies the equation
Ax" (t) + x' (t) + x(t) = 0 for 0 < t < 2π.
For no.1, I think its when t=0, because within the interval 0 ≤ t ≤ 2pi, 0 is when x has the least value, therefore most to the left.
For no.2, x(t)= e-t sin t, x'(t)= e-t (cos t - sin t), and x''(t)= -2e-t cos t. Factorizing, x(t)+x'(t)+x''(t) gives me e-t (sin t +cos t -sin t -2A cos t). To make the sums inside parentheses zero, A would have fit the condition 0= cos t - 2A cos t. A= [tex]\frac{1}{2}[/tex] fits, it seems.
Am I on the right track? Thanks
The question is:
A particle moves alonge the x-axis with position at time t given by x(t) = e^(-t) sin t for 0 ≤ t ≤ 2π.
1. Find the time t at which the particle is farthest to the left. Justify your answer.
2. Find the value of the constant A for which x(t) satisfies the equation
Ax" (t) + x' (t) + x(t) = 0 for 0 < t < 2π.
For no.1, I think its when t=0, because within the interval 0 ≤ t ≤ 2pi, 0 is when x has the least value, therefore most to the left.
For no.2, x(t)= e-t sin t, x'(t)= e-t (cos t - sin t), and x''(t)= -2e-t cos t. Factorizing, x(t)+x'(t)+x''(t) gives me e-t (sin t +cos t -sin t -2A cos t). To make the sums inside parentheses zero, A would have fit the condition 0= cos t - 2A cos t. A= [tex]\frac{1}{2}[/tex] fits, it seems.
Am I on the right track? Thanks