376m/s(must be (-) because the velocity vector is pointing down).---------------4)max kinetic energy of body is 1/2 mv^2= max spring energy = 1/2 kA^2mv^2 = kA^2find k:T = 2pi*√(m/k)2 = 2pi*√(m/k)(1/pi)^2 = m/kk = m/(1/pi)^2mv^2 = m/(1/pi)^2*A^2v^2 = A^2/(1/pi)^21 = A^2/(1/pi)^2A^2 = (1/pi)^2A = 1/piA = 0.318 malternatively and easier:equation is y = A*sin(pi*t)v = A*pi*cos(pi*t)and when the body goes through the equilibrium point, then t = n*2with n an integer.with n = 1--> t = 2v = A*pi*cos(2pi)v = A*pi*11 = A*piA = 1/pi A = 0.318 mRegards-Ill answer 3).......
4pi*t = cos^-1(0.8)
t = 0.0512 s
equation for v is
v = -0.05*4pi*sin(4pi*0.0512)
v = -0.376 m/s (must be (-) because the velocity vector is pointing down).
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4)
max kinetic energy of body is 1/2 mv^2
= max spring energy = 1/2 kA^2
mv^2 = kA^2
find k:
T = 2pi*√(m/k)
2 = 2pi*√(m/k)
(1/pi)^2 = m/k
k = m/(1/pi)^2
mv^2 = m/(1/pi)^2*A^2
v^2 = A^2/(1/pi)^2
1 = A^2/(1/pi)^2
A^2 = (1/pi)^2
A = 1/pi
A = 0.318 m
alternatively and easier:
equation is
y = A*sin(pi*t)
v = A*pi*cos(pi*t)
and when the body goes through the equilibrium point, then t = n*2 with n an integer.
with n = 1--> t = 2
v = A*pi*cos(2pi)
v = A*pi*1
1 = A*pi
A = 1/pi
A = 0.318 m
Regards
I'll answer 3).
x = 5 cos(2(pi)nt + p)
n = 2
x = 5 cos(4(pi)nt + p)
v = -20(pi) sin(4(pi)t + p)
x = 5 and v = 0 when t = 0
therefore p = 0
x = 4 when 5 cos(4(pi)t) = 4
cos(4(pi)t) = 0.8
sin(4(pi)t) = 0.6
v = -12(pi)
i.e. downwards 37.7 cm/s, or 0.38 m/s
Given answer almost correct.
