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sasho [114]
3 years ago
9

A block is set in motion hanging from a spring and oscillates about its resting position

Mathematics
2 answers:
coldgirl [10]3 years ago
8 0

Answer:

t = 1.277 sec and t = 2.848 sec

Step-by-step explanation:

This problem is much more easily done by graphing it than by computing it using algebra.

The values of t we're looking for are the ones that make x = 0, so we want the solutions of 0.6sin(2t)+0.4cos(2t)=0 on the interval [0, 3].

According to the graph, this is true when t = 1.277 seconds and t = 2.848 seconds.

Paha777 [63]3 years ago
6 0

Answer:

t = 1.28, 2.85

Step-by-step explanation:

x = 0.6sin(2t)+0.4cos(2t)

x = 0, so

0.6sin(2t)+0.4cos(2t) = 0

0.6sin(2t) = -0.4cos(2t)

Convert into tan(2t) by dividing both sides by 0.6cos(2t):

tan(2t) = -0.4/0.6

tan(2t) =-2/3

Since t lies in [0,3] ,

2t lies in [0,6]

tan(2t) =-2/3

Basic angle:

0.5880026035

Tan is negative is second and fourth quadrants

2t = 2.553590005, 5.695182704

t = 1.276795025, 2.847591352

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