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Explanation:
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Answer:
(a) A = 0.700m
(b) k = 80.6N/m
(c) x = -0.699m
(d) x = -0.350m
(e) t = 0.168s
Explanation:
Given the equation of motion for the spring
X = 0.700cos(12.0t), m = 0.56kg
(a) A = amplitude = 0.700m
(b) The angular velocity ω = 12rad/s
ω = √(k/m)
ω² = k/m
k = m×ω² = 0.56×12² = 80.6N/m
Spring constant k = 80.6N/m
(c) T = 2π/ω = 2π/12
T = 0.524s
At t = T/2 = 0.524/2 = 0.262s
So x = 0.700cos(12×0.262) = –0.699m
(d) At t = 2/3×T = 2×0.524/3 = 0. 349s
x = 0.700cos(12×0.349) = –0.350m
(e) to find t at x = -0.300m
–0.300 = 0.700cos(12t)
–0.300/0.700 = cos(12t)
cos(12t) = –0.429
12t = cos-¹(-0.429)
12t = 2.01
t = 2.01/12
t = 0.168s
True
The rate at which work is done is referred to as power. A task done quite quickly is described as having a relatively large power. The same task that is done more slowly is described as being of less power. Both tasks require he same amount of work but they have a different power.
"increments of 8" means the major divisions are 0,8,16,24 ?
<span>x axis, calculate the moment arms from 0 </span>
<span>3x4, 2x12, 1x20 </span>
<span>from an arbitrary C </span>
<span>3(c-4) + 2(c-12) + (c-20) = 0 </span>
<span>3c - 12 + 2c -24 + c - 20 = 0 </span>
<span>6c = 56 </span>
<span>c = 9.33 </span>
<span>y axis </span>
<span>3x3, 1x12, 2x20 </span>
<span>3(c-4) + 1(c-12) +2 (c-20) = 0 </span>
<span>3c - 12 + c - 12 + 2c - 40 = 0 </span>
<span>6c = 64 </span>
<span>c = 10.67 </span>
<span>so center is x = 9.33, y = 10.67 </span>
