An object, attached to the end of a horizontal spring, oscillates with simple ha

Question

An object, attached to the end of a horizontal spring, oscillates with simple harmonic motion along the x axis. Its displacement varies with time according to the equation x = (5cm) cos (2t ). What are: a) The position of the object at t=1.0 s b) The velocity (in m/s) of the body at t = 1.0 s c) The acceleration of the body at t=1.0 s. d) Amplitude of the oscillation. e) Period of the oscillation. f) Maximum speed of the body. An object, attached to the end of a horizontal spring, oscillates with simple harmonic motion along the x axis. Its displacement varies with time according to the equation x = (5cm) cos (2t ). What are: a) The position of the object at t=1.0 s b) The velocity (in m/s) of the body at t = 1.0 s c) The acceleration of the body at t=1.0 s. d) Amplitude of the oscillation. e) Period of the oscillation. f) Maximum speed of the body. An object, attached to the end of a horizontal spring, oscillates with simple harmonic motion along the x axis. Its displacement varies with time according to the equation x = (5cm) cos (2t ). What are: a) The position of the object at t=1.0 s b) The velocity (in m/s) of the body at t = 1.0 s c) The acceleration of the body at t=1.0 s. d) Amplitude of the oscillation. e) Period of the oscillation. f) Maximum speed of the body.

Explanation / Answer

Here ,

x = (5 cm ) * cos(2t)

amplitude , A = 5 cm = 0.05 m

w = 2 rad/s

a) at t = 1 s

x = 5 * cos(2)

x = -2.08 cm

the position at t = 1 is -2.08 cm

b)

velocity = dx/dt

velcoity = 5 * 2 * (-sin(2*1))

velcoity = 9.09 cm/s

the velocity at t = 1 s is 9.09 cm/s

c)

acceleration , a = -x*w^2

a = 2.08 * (2)^2

a = 8.32 cm/s^2

the accleration of body is 8.32 cm/s^2

d)

ampilutde of motion , A = 5 cm

e)

time period = 2 *pi/w

time period = 2 * pi/2

time period = 3.141 s

the time period of body is 3.141 s

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