# physics

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Objects of equal mass are oscillating up and down in simple harmonic motion on two different vertical springs. The spring constant of spring 1 is 186 N/m. The motion of the object on spring 1 has 3 times the amplitude as the motion of the object on spring 2. The magnitude of the maximum velocity is the same in each case. Find the spring constant of spring 2.

My work...

Aw=Aw
A(sqrt of k/m) = A(sqrt k/m)
(sqrt of 186) = 3 (sqrt of k)
(sqrt of 186)/3 = (sqrt of k)
[(sqrt of 186)/3] ^2 = k

• physics -

body 1
x = sin 2 pi f t
v = 2 pi f cos 2 pi f t
a = -(2pi)^2 f^2 sin 2 pi f t
-k x = m a
- k x = - m(2pi)^2 f^2 sin 2 pi f t
- k/m = - (2 pi)^2 f^2
f = (1/2pi) sqrt(k/m)

body 2
x = 3 sin 2 pi F t
v = 3 (2 pi) F cos 2 pi F t
- K/m = -3 (2 pi)^2 F^2 sin 2 pi F t
-K/m =-(2 pi)^2 F^2
F = (1/2pi) sqrt(K/m)

the to v values are equal in magnitude
2 pi f = 6 pi F

2 pi ((1/2pi) sqrt(k/m)= 6 pi(1/2pi) sqrt(K/m)

sqrt(k/m) = 3 sqrt(K/m)
k/m = 9 K/m
K = k/9 = 20.67

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