mass of 0.400 kg is attached to a spring and set into oscillation on a horizontal frictionless surface. The simple harmonic motion of the mass is described by x(t) = (0.700 m)cos[(20.0 rad/s)t]. Determine the following. (a) amplitude of oscillation for the oscillating mass ______ m (b) force constant for the spring ______ N/m (c) position of the mass after it has been oscillating for one half a period ______ m (d) position of the mass one-third of a period after it has been released ______ m
mass of 0.400 kg is attached to a spring and set into oscillation on a horizontal frictionless surface. The simple harmonic motion of the mass is described by x(t) = (0.700 m)cos[(20.0 rad/s)t]. Determine the following. (a) amplitude of oscillation for the oscillating mass ______ m (b) force constant for the spring ______ N/m (c) position of the mass after it has been oscillating for one half a period ______ m (d) position of the mass one-third of a period after it has been released ______ m
mass of 0.400 kg is attached to a spring and set into oscillation on a horizontal frictionless surface. The simple harmonic motion of the mass is described by x(t) = (0.700 m)cos[(20.0 rad/s)t]. Determine the following. (a) amplitude of oscillation for the oscillating mass ______ m (b) force constant for the spring ______ N/m (c) position of the mass after it has been oscillating for one half a period ______ m (d) position of the mass one-third of a period after it has been released ______ m
A mass of 0.400 kg is attached to a spring and set into oscillation on a horizontal frictionless surface. The simple harmonic motion of the mass is described by x(t) = (0.700 m)cos[(20.0 rad/s)t]. Determine the following.
(a) amplitude of oscillation for the oscillating mass ______ m
(b) force constant for the spring ______ N/m
(c) position of the mass after it has been oscillating for one half a period ______ m
(d) position of the mass one-third of a period after it has been released ______ m
(e) time it takes the mass to get to the position x = −0.100 m after it has been released ______ s
Transcribed Image Text:A mass of 0.400 kg is attached to a spring and set into oscillation on a horizontal frictionless surface. The simple harmonic motion of the mass is described by
x(t) = (0.700 m) cos[(20.0 rad/s)t]. Determine the following.
(a) amplitude of oscillation for the oscillating mass
m
(b) force constant for the spring
N/m
(c) position of the mass after it has been oscillating for one half a period
m
(d) position of the mass one-third of a period after it has been released
m
(e) time it takes the mass to get to the position x = -0.100 m after it has been released
Definition Definition Special type of oscillation where the force of restoration is directly proportional to the displacement of the object from its mean or initial position. If an object is in motion such that the acceleration of the object is directly proportional to its displacement (which helps the moving object return to its resting position) then the object is said to undergo a simple harmonic motion. An object undergoing SHM always moves like a wave.
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Follow-up Question
I am confused with part (e). I don't understand the steps. How is 1.427 obtained? How is the 20t moved to the left side of the equation, since it is inside the COS() function? I am just not understanding the math. Can you step it through with an explanation at each individual step?
Transcribed Image Text:e)
x = 0.7 COS(20.t)
0.1 = 0.7 cos (20+)
20t=1.427 Rad.
+= 0·07 sec
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![A mass of 0.400 kg is attached to a spring and set into oscillation on a horizontal frictionless surface. The simple harmonic motion of the mass is described by
x(t) = (0.700 m) cos[(20.0 rad/s)t]. Determine the following.
(a) amplitude of oscillation for the oscillating mass
m
(b) force constant for the spring
N/m
(c) position of the mass after it has been oscillating for one half a period
m
(d) position of the mass one-third of a period after it has been released
m
(e) time it takes the mass to get to the position x = -0.100 m after it has been released](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7c560a1a-db76-4fd0-82f5-78bd443b8157%2F54902f8d-8d4b-417c-a9e4-efccb741a14c%2Fak804yn_processed.jpeg&w=3840&q=75)
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