Question

Question: A block with mass of m = 3.78 kg is attached to springs with spring constants of ki = 18.1 N/m and k = 25.6 N/m, in different configurations shown in the figures below. Assume in all these cases that friction is negligible. Part 1) You will need to calculate the period of oscillations for each situation In this situation the mass is connected between the two springs which are each connected to opposite walls (Figure 1). What is the period of oscillations in this case? k1 k2 WWW ww m Figure 1: A mass, m. connected to opposite walls via two springs opposite sides with spring constants of k, and kr. The first spring is to the left of the mass the second is to the right T Part 2) The two springs are now both on the same side of m and both connect (Figure 2). What is the period of these oscillations? to the wall m Figure 2: A mass, m, connected on its left-hand side to a single wall via two springs on the same side with spring constants of ki and ks. T Part 3) The two springs are now connected to each other Figure 3. The first spring is connected to the wall and the second spring to the mass. What is the period of these oscillations? ki kz www Figure 3: A mass, m, connected on its left-hand side to a single wall via two Springs with spring constants of k, and k. The springs are connected to each other. The first spring is directly connected to the wall and the second ring is directly connected to the mass. Check

Answer 1

Part-o Both springs are in parallel combination kag = kitke T: 20 m 3.78 T= 2x3.14. - 18.1 +25-6 TT = 1.8460 Part Combination spring are in parallel Keq=kithe F = 1.8465 / Part ① Springs are in series Combination Keg Kille - 18.1825.6 - 10.603 с ии. &J + 23-6 T: 243. T= 3.749]