[2] Let's consider the block-spring system as shown in the following figure. From Newton's low, the...

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[2] Let's consider the block-spring system as shown in the following figure. From Newton's low, the equation of motion in this system is given by ma = -kx, where a is the acceleration, k is the spring constant, and m is the mass of the block. An x axis has been placed parallel to the length of the spring, with the origin (x = 0) at the position of the free end when the spring is in its relaxed state. 10000 [2-1] Derive the angular frequency wo of the system (it is called natural frequency). [2-2] Let's consider the case when a damping force is applied to the block. The damping force is proportional to the velocity v. The damping constant is given by b. (2-2-1) Derive the equation of motion of this system. (2-2-2) Now, the displacement of the block in this system is given by Xp (t)= xmet/ cos wt. Derive 7 and in the above equation. The process of deriving them should be also shown. (2-2-3) Derive the ratio of the amplitude just when one period has passed to the one when t = 0. [2-3] Let's consider the case when an external force is applied to the block to cause the driven oscillation. Now, the external force is given by F(t)= Focos wt. Note that the damping force does not exist, now. (2-3-1) Derive the equation of motion of this system. (2-3-2) Now, the displacement of the block in this system is given by XF(t) = X cos wt. Derive the displacement amplitude of the block Xin this system. The process of deriving them should be also shown. (2-3-3) Draw the figure which shows how the displacement amplitude Xof the block in this system depends on a normalized angular frequency w/wo, where wo is the natural frequency derived in [2-1]. [2] Let's consider the block-spring system as shown in the following figure. From Newton's low, the equation of motion in this system is given by ma = -kx, where a is the acceleration, k is the spring constant, and m is the mass of the block. An x axis has been placed parallel to the length of the spring, with the origin (x = 0) at the position of the free end when the spring is in its relaxed state. 10000 [2-1] Derive the angular frequency wo of the system (it is called natural frequency). [2-2] Let's consider the case when a damping force is applied to the block. The damping force is proportional to the velocity v. The damping constant is given by b. (2-2-1) Derive the equation of motion of this system. (2-2-2) Now, the displacement of the block in this system is given by Xp (t)= xmet/ cos wt. Derive 7 and in the above equation. The process of deriving them should be also shown. (2-2-3) Derive the ratio of the amplitude just when one period has passed to the one when t = 0. [2-3] Let's consider the case when an external force is applied to the block to cause the driven oscillation. Now, the external force is given by F(t)= Focos wt. Note that the damping force does not exist, now. (2-3-1) Derive the equation of motion of this system. (2-3-2) Now, the displacement of the block in this system is given by XF(t) = X cos wt. Derive the displacement amplitude of the block Xin this system. The process of deriving them should be also shown. (2-3-3) Draw the figure which shows how the displacement amplitude Xof the block in this system depends on a normalized angular frequency w/wo, where wo is the natural frequency derived in [2-1].

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For un damped use 21 is ma R kx which Cen be wonten 4 the equeren of Mitu 22 rearrange he squetun to ... View the full answer