## 1 Introduction  
In recent years, the introduction of advanced materials and innovative designs has led to the creation of Energy Storing And Return (ESAR) prosthetic feet, which better replicate the natural functions of the limb, given the improved energy storage and return properties [1]. The ESAR feet are typically made of carbon fibre composites due to their light weight, exceptional strength, and good chemical properties, which contribute to the component's durability. Additionally, they exhibit minimal deformation under varying loads compared to materials like aluminium and titanium alloys [2], and they provide a good spring-like [3, 4] effect. Such prosthetics also confer better symmetry to the gait and they improve the subject's comfort and reactivity [5]. Last but not least, an important advantage of composite materials is that they can be \"tailor made\", allowing for precise control over the mechanical behaviour of the components [6; 7; 8]. Improvements in prosthetic technology have led to the development of specialised sport-purpose feet, the blade prostheses [9; 10; 11]. These ESAR feet are specifically optimised for high-level sports, fulfilling the unique demands and requirements of athletes. They provide improved performance, stability, and responsiveness, allowing athletes with limb loss to engage in different sports activities at a competitive level. Several studies proposed advances [12], challenges [13; 14], and future perspectives [15] on lower limb prosthetic technology since the insight of its mechanical behaviour is essential for their proper design, development, and customisation, to optimally meet individual requirements [16]. Different research works can be found in the literature, treating various topics, such as static analysis of prosthesis technology used in elite sport [17; 18] or for running [19; 20; 21], in order to evaluate the stiffness characteristics [22] of blade prosthetics, or the investigation of their dynamic performance [23; 24]; other studies propose the development of wearable sensors for mapping the behaviour of energy storing and returning in prosthesis [25; 26], and the assessment of the influence of different composite material in the performance of athletes with prostheses [8; 27; 28]. Indeed, no standardised tests are currently available to achieve a full characterisation of the mechanical behaviour of the blade prosthetic in operating conditions [29]. As pointed out from the research of [PERSON] et al. [20; 21], the running prostheses stiffness is affected by multiple factors. Indeed, when the speed increases from 3 m/s, the stiffness decreases. Furthermore, the dimension of the prosthetic affects the proximal bending moment value and thus the vertical displacement, resulting in different stiffness values. Above all, due to conflicting evidence in the literature and the insufficient information provided by the manufacturers, it is uncertain if the force-displacement profile is considered linear or curvilinear. For example, the mechanical tests of [PERSON] et al. [19] on Elite Blade prostheses demonstrate that the stiffness is load-dependent. The knowledge of the stiffness behaviour in correspondence to the peak of the force is important to understand the component performance, but its dynamic modal analysis also plays a pivotal role in unravelling the intricate mechanical and performance characteristics of the prosthetic devices. This analysis implies the identification and examination of the natural frequencies, mode shapes, and damping ratios of the foot blade prosthetics. Few works have been conducted with this purpose [30; 31; 32; 33; 34; 35; 36]. The correlation between the dynamic behaviour of prosthetic blades with the mass they carry is explored in [31; 33]. Both studies employed a T-shaped steel mounting bracket to apply the masses to the prosthetics. The bracket was carefully fixed to ensure that the line of action of the masses aligned with the ground reaction point of the foot, preventing any rotational effects.