Please help!! 1) An air-track glider is attached to a spring. The glider is pull

Question

Please help!!

1)An air-track glider is attached to a spring. The glider is pulled to the right and released from rest at t=0 s. It then oscillates with a period of 1.50sand a maximum speed of 56.0cm/s

What is the glider's position at t= 28.0s ?

2)A spring with spring constant 20N/m hangs from the ceiling. A ball is attached to the spring and allowed to come to rest. It is then pulled down 9.5cm and released. The ball makes 33 oscillations in 24s seconds

What is its maximum speed? Express your answer to two significant figures and include the appropriate units

3)

An air-track glider is attached to a spring. The glider is pulled to the right and released from rest at t=0 s. It then oscillates with a period of 1.50sand a maximum speed of 56.0cm/s What is the glider's position at t= 28.0s ? A spring with spring constant 20N/m hangs from the ceiling. A ball is attached to the spring and allowed to come to rest. It is then pulled down 9.5cm and released. The ball makes 33 oscillations in 24s seconds What is its maximum speed? Express your answer to two significant figures and include the appropriate units

Explanation / Answer

1) x = Asin(wt)

T = 2pi/w

1.5 = 2pi/w

w = 4.19 rad/s

v =dx/dt = Awcos(wt)

vmax occurs when |cos(wt)| = 1,

So, wt = n*pi

0.56 = Aw

A = 0.133m

At t=28sec,

Glider's position = Asin(wt) = 0.133sin(4.19*28*180/pi) = -0.117m = -11.7cm

2) T = 24/33s = 0.727s

T = 2pi/w

0.727 = 2pi/w

w = 8.64 rad/s

vmax = Aw = 0.095*8.64 = 0.8208m/sec

3) T = 12s

T = 2pi/w

12 = 2pi/w

w = 0.5236 rad/s

vmax = Aw

0.60 = A*0.5236

A = 1.1459m

v = Awcos(wt + phi)

At vmax, cos(wt + phi) = 1

cos(0.5236*4 + phi) = 1

cos(2.0944 + phi) = 1

phi = 4.188 rad

position at t=0: x = Asin(wt +phi) = 1.1459sin(4.188) = -0.9923m

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