Mechanical engineers often study the movement of damped oscillating objects. Studies of this type play an important role
Posted: Tue Jul 12, 2022 8:48 am
Mechanical engineers often study the movement of damped oscillating objects. Studies of this type
play an important role in the design of automobiles suspensions, among other things. The horizontal
displacement of an object is given as a function of time by the equation
𝑥 = 𝑥0 𝑒−βt[cos(𝜔𝑡) + 𝛽 sin(𝜔𝑡)]
𝜔
The parameters 𝛽 and 𝜔 depend upon the mass of the object and the dynamic characteristics of the
system.
Prepare a table of 𝑥 versus 𝑡 over the interval 0 ≤ 𝑡 ≤ 30 seconds, using the formula-copying technique
illustrated in Example 3.2 of the textbook. When entering formulas, be careful to use relative and
absolute cell addressing correctly, as required. To construct the table, assume 𝑥0 = 9.5 in, 𝛽 =
0.2 sec−1, and 𝜔 = 0.3 sec−1. Use 1-second intervals (i.e., let 𝑡 = 0, 1, 2, ... , 30 seconds). Estimate the
point where 𝑥 first crosses the 𝑡-axis (i.e., estimate the value of 𝑡 corresponding to 𝑥 = 0).
play an important role in the design of automobiles suspensions, among other things. The horizontal
displacement of an object is given as a function of time by the equation
𝑥 = 𝑥0 𝑒−βt[cos(𝜔𝑡) + 𝛽 sin(𝜔𝑡)]
𝜔
The parameters 𝛽 and 𝜔 depend upon the mass of the object and the dynamic characteristics of the
system.
Prepare a table of 𝑥 versus 𝑡 over the interval 0 ≤ 𝑡 ≤ 30 seconds, using the formula-copying technique
illustrated in Example 3.2 of the textbook. When entering formulas, be careful to use relative and
absolute cell addressing correctly, as required. To construct the table, assume 𝑥0 = 9.5 in, 𝛽 =
0.2 sec−1, and 𝜔 = 0.3 sec−1. Use 1-second intervals (i.e., let 𝑡 = 0, 1, 2, ... , 30 seconds). Estimate the
point where 𝑥 first crosses the 𝑡-axis (i.e., estimate the value of 𝑡 corresponding to 𝑥 = 0).