Final Answer:
(a) Amplitude A = 0.2 m
(b) Angular Frequency
rad/s
(c) Spring Constant k = 4 N/m
(d) Speed at
m/s
(e) Acceleration at t = 2.0 s = 0.8 m/s²
Step-by-step explanation:
The amplitude (A) of the motion is the maximum displacement from the equilibrium position. In the given drawing, the amplitude is the distance from the equilibrium position to the maximum displacement, which is 0.2 meters.
The angular frequency
can be determined from the period of oscillation. Since the period
is the time taken for one complete oscillation and is given by
, solving for
yields
rad/s.
The spring constant (k) is related to the angular frequency by
, where m is the mass. Solving for k gives k = 4 N/m.
To find the speed at t = 2.0 s, we can use the equation
, where A is the amplitude and
is the angular frequency. Substituting the given values, we get v = 0.4 m/s.
Finally, the magnitude of acceleration at t = 2.0s is given by
. Substituting the known values, we find \( a = 0.8 \) m/s². These calculations provide a comprehensive understanding of the motion of the mass attached to the spring at various points in time.