3) A 3 kg mass is attached to the end of a horizontal spring, with k = 1500 N/m. The mass is pulled out to x= 2 m from its equilibrium position, then let go. Assume the surface is frictionless, k= 1500 N/m X₁ = 2 m a) What is the spring force before it is released and the acceleration immediately after it is released? - 300 F. =_ 1500(2) 300/3 b) What are each of the following before the mass is released? 30 PEP N PE, p = E₁ = 30 30+0=30 ½(1500) (-2)² e) What are each of the following as the mass passes through the equilibrium position, x = 0? Some of these will be in terms of variables. O J. Vm= wxm a = 100 KE, = m = 3 kg -5 (3)(0) J. KE = 1.5veg ² J. -5(3)veq² d) Using conservation of energy, find the speed of the mass as it passes through equilibrium x = 0. 4.47 Celana Park of 2 •Sveq² =30 e) What are the frequencies and period of the motion? 1=3.56 veg²-20=√√√20 = 4.47 217 J. = 22.36 rad/sec JK --√√1500 22.36 277=6.28 3 f) What are maximum values of the velocity and acceleration? These should be familiar. 100 m/s² am E = Hz 1.5 veg². =Wvm T= 0.281 sec. 7/-3/56 =

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3) A 3 kg mass is attached to the end of a horizontal spring, with k = 1500 N/m. The mass is pulled out
to x = 2 m from its equilibrium position, then let go. Assume the surface is frictionless.
X₁ = 2 m
a) What is the spring force before it is released and the acceleration immediately after it is released?
Fap
k= 1500 N/m
- 300
1500(2)
b) What are each of the following before the mass is released?
30
N
PE, sp =
E₁ = 30
30+0=30
2 (1500) (-2)²
c) What are each of the following as the mass passes through the equilibrium position, x = 0?
Some of these will be in terms of variables.
PE sp =
Vm=
J.
wxm
m/s
a = 100
300/3
J.
KE₁ =
1.5 veg ² J.
5(3)veq²
d) Using conservation of energy, find the speed of the mass as it passes through equilibrium x = 0.
trength euildrian x = ਹੈ।
4.47
m = 3 kg
.5 (3)(0)
KE =
2
Sveq² =30
veq
e) What are the frequencies and period of the motion?
1=3.56
201
J.
1²= 20 = √√√20=4.47
=
22.36 rad/sec
=√J K = -√ √ 1500
22.36
277=6.28
3
f) What are maximum values of the velocity and acceleration? These should be familiar.
100
m/s²
a =
Eq=
Hz
1.5 veq²
am = wvm
T= 0.281
귿
J.
=
356
Transcribed Image Text:3) A 3 kg mass is attached to the end of a horizontal spring, with k = 1500 N/m. The mass is pulled out to x = 2 m from its equilibrium position, then let go. Assume the surface is frictionless. X₁ = 2 m a) What is the spring force before it is released and the acceleration immediately after it is released? Fap k= 1500 N/m - 300 1500(2) b) What are each of the following before the mass is released? 30 N PE, sp = E₁ = 30 30+0=30 2 (1500) (-2)² c) What are each of the following as the mass passes through the equilibrium position, x = 0? Some of these will be in terms of variables. PE sp = Vm= J. wxm m/s a = 100 300/3 J. KE₁ = 1.5 veg ² J. 5(3)veq² d) Using conservation of energy, find the speed of the mass as it passes through equilibrium x = 0. trength euildrian x = ਹੈ। 4.47 m = 3 kg .5 (3)(0) KE = 2 Sveq² =30 veq e) What are the frequencies and period of the motion? 1=3.56 201 J. 1²= 20 = √√√20=4.47 = 22.36 rad/sec =√J K = -√ √ 1500 22.36 277=6.28 3 f) What are maximum values of the velocity and acceleration? These should be familiar. 100 m/s² a = Eq= Hz 1.5 veq² am = wvm T= 0.281 귿 J. = 356
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