A ball is attached by two springs as shown in the left figure( |wwOww| ).If the mass is displaced a distance ⊿x below the equilibrium position h. Determine whether vertical SHM is possible for the system shown. If so, find the natural frequency. [assume that the vertical extension ⊿x is corrspond with the extended length d' of the spring and (1 + a)to the power of -b is close to 1-ab if a is small.]
What does the symbol ⊿ supposed to represent?
Are the springs arranged horizontally?
Sorry about that....⊿x means a small distance x, i can't find a perfect triangle.
Since the mass have weight, the springs is not arranged horizontally in equilibrium position.
It can be explained more clearly if i can send you a diagram.
Like this:
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To determine whether vertical Simple Harmonic Motion (SHM) is possible for the given system, we need to check if the restoring force is proportional to the displacement and acts in the opposite direction.
In the given system, the ball is attached by two springs, which suggests that there will be two restoring forces acting on the ball in the vertical direction. Let's analyze each spring's restoring force individually:
1. Upper Spring: When the ball is displaced downward, the upper spring is stretched, resulting in an upward force. This restoring force opposes the displacement, indicating a viable possibility for SHM.
2. Lower Spring: When the ball is displaced downward, it compresses the lower spring, resulting in a downward force. This restoring force acts in the same direction as the displacement, which does not support SHM.
Based on the behavior of the springs, it can be concluded that vertical SHM is not possible for the given system. The restoring forces acting on the ball are not proportional to the displacement and do not act in the opposite direction.
As a result, there is no natural frequency for this system since it does not exhibit vertical SHM.