The position of a 54 {\ m g} oscillating mass is given by x\\,(t)\\;=\\; ( 2.5 c

Question

The position of a 54 { m g} oscillating mass is given by x,(t);=; ( 2.5 cm ),cos 10 t, where t is in seconds.

Part A -
Determine the amplitude in cm.
Express your answer using two significant figures.


Part B -
Determine the period in s.
Express your answer using two significant figures.

Part C -
Determine the spring constant in N/m
Express your answer using two significant figures.

Part D -
Determine the maximum speed in m/s.
Express your answer using two significant figures.

Part E -
Determine the total energy in J.
Express your answer using two significant figures.

Part F -
Determine the velocity at t1 = 3.9×10-2 s. In m/s.
Express your answer using two significant figures.

Explanation / Answer

mass m = 54 g = 0.054 kg
position x = (2.5 cm) cos10t    ........ (1) here, angular speed = 10 rad/s          amplitude A = 2.5 cm a) amplitude A = 2.5 cm b) period T = 2/               = (2)(3.14) / (10 rad/s)              = 0.628 s c) spring constant k = 2m      (since, = k/m)                            = (10 rad/s)2(0.054 kg)                            = 5.4 N/m d) maximum speed v = A                             = (2.5*10-2 m)(10 rad/s)                             = 2.5 m/s e) total energy E = (1/2)kA22                       = (1/2)(5.4 N/m)(2.5*10-2 m)2                        = 16.87*10-4 J f) position x = (2.5 cm) cos10t    velocity v = dx/dt                = -(2.5 cm)(10) sin10t   at t = 3.9×10-2 s , the velocity is              v = -(2.5*10-2 m)(10) sin(10*3.9×10-2 s)                 = -9.5*10-2 m/s                   = -0.095 m/s magnitude , v = 0.095 m/s ----------------------------------------------- note/: here i can take calcultaion of sine function in radians.                       = (1/2)(5.4 N/m)(2.5*10-2 m)2                        = 16.87*10-4 J f) position x = (2.5 cm) cos10t    velocity v = dx/dt                = -(2.5 cm)(10) sin10t   at t = 3.9×10-2 s , the velocity is              v = -(2.5*10-2 m)(10) sin(10*3.9×10-2 s)                 = -9.5*10-2 m/s                   = -0.095 m/s magnitude , v = 0.095 m/s ----------------------------------------------- note/: here i can take calcultaion of sine function in radians.

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